The hosts made the breakthrough thanks to a goal from Chancel Mbemba but Nemanja Matic made sure Benfica went into the break level by heading home from a Nicolas Gaitan free kick.
Benfica were handed the lead in the 52nd minute when Mbemba inadvertently deflected the ball into his own net.
It looked like Anderlecht had rescued a point when Massimo Bruno fired in an equaliser but Rodrigo secured the vital victory for Benfica with a winner in the final minute.
Read below to find out how the drama unfolded.
6.45pmGood evening everyone. Just two games left for each team in the Champions League group stages. Anderlecht and Benfica can both still reach the knockout stages, but who will take a step closer tonight?
6.48pmIt's a very big ask for Anderlecht to qualify from Group C. They must win their final two games to have any chance of playing Champions League football in February.
6.50pmA draw would secure third spot for Benfica, but that won't be their target. They'll join Olympiacos on seven points if they win tonight and the Greek club lose to Paris Saint-Germain, who are currently top on 10 points.
6.52pmAnderlecht chances of qualifying may be slim but there's another target they'll want to reach in Group C. The Belgian club have finished bottom in each of their previous six campaigns in this competition.
6.55pmANDERLECHT: Proto, N'Sakala, Deschacht, Nuytinck, Kouyate, Mbemba, Vanden Borre, Praet, Gillet, Bruno Mitrovic
SUBSTITUTES: Kaminski, De Zeeuw, Milibojevic, Tielemans, Vargas, Najar, Acheampong
7.00pmDangerous midfielder Sacha Kljestan misses tonight game due to his red card against Paris Saint-Germain on matchday four, which means Anderlecht will mainly be relying on youngster Aleksandar Mitrovic to provide goals.
7.03pmI'm sure you've noticed the big absence from Benfica's lineup. Oscar Cardozo sits out due to a back problem, so it's the battle of the promising Serbians as Lazar Markovic starts for Benfica. A lot will be expected of Lima, who should provide the main goal threat for the visitors.
7.05pmDennis Praet will probably start in a central role behind Mitrovic, while Cheikhou Kouyaté is expected to play in midfield to make up for Kljestan's absence.
7.09pmAnderlecht have picked up just one point from their first four games in this season's competition but a fiery atmosphere is likely to make it difficult for Benfica this evening. The Portuguese club desperately need a win as they face PSG in their final game.
7.11pmCardozo is a big loss but Benfica simply cannot allow that to be used as an excuse this evening. They suffered heartbreak last year when they finished third in their group but anything other than a win could condemn them to the same fate.
7.15pmIn two Champions League home games this season, Anderlecht have conceded eight goals and scored none. Not good signs for the home supporters ahead of tonight's game.
7.17pmBenfica's problem in the group stage has also been goals. They've scored just three times in four games and Cardozo's absence could make it even more difficult for the visitors.
7.23pmAn interesting choice from Jorge Jesus this evening is to play Ljuobmir Fejsa in midfield instead of the more creative Filip Djuricic. The Serbian could be dangerous off the bench for the visitors, which may be what the Benfica boss has in mind.
7.27pmAnderlecht are currently fifth in the Belgian league, six points behind leaders Standard Liege. It's going to be difficult domestically this season but a strong display tonight could boost confidence.
7.30pmPREDICTION: Just 15 minutes until kick off, so it's time guess what the score will be this evening. I think Anderlecht can cause Benfica problems tonight but Benfica should have enough to secure all three points. 3-1 to the visitors.
7.33pmIt's probably fair to say that we haven't seen the best of Benfica in the group stages. They were impresseive against Olympiacos a couple of weeks ago, though and that improved display probably deserved three points.
7.35pmGaitan and Markovic are the key men for Benfica tonight. If they can cause the problems on the wings, Cardozo's absence may not prove to be as important.
7.39pmThe players are in the tunnel now as the atmosphere builds inside the ground. Just a few minutes before the action begins.
7.42pmBoth sets of players shake hands with their rivals as a banner reading 'You are not alone, Philippines' is displayed. You'll see that message across Europe this week.
7.44pmHere we go. Anderlecht will get the game underway.
1 minAnderlecht are immediately on the front foot as Benfica are forced to defend a couple of dangerous deliveries into the box.
3 minIt's been a very fast start to the game in Belgium, with both teams eager to take control early on. We could be treated to a very open contest.
4 minAlmeida unleashes the first shot after cutting in from the left wing but his effort drifts well wide of the target.
5 minPlenty of tackles flying in from both sides but neither team have been able to hang on to possession for long enough to build pressure.
7 minBenfica are beginning to settle into a good passing rhythm but their task is being made difficult by Anderlecht's pressing game. Markovic has been eager to cut inside in the early stages.
9 minIt's been an impressive start by the hosts, with their young players showing off their determination to impress by pressing high up the pitch.
11 minMitrovic is clearly a concern for what looks like a nervy Benfica defence as he collects the ball on the edge of the box before losing control at the crucial moment.
12 minSHOT! Gaitan links well with Almeida on the left and the ball eventually arrives to Lima, who drills an effort wide from 25 yards.
14 minUPDATE! PSG have taken the lead in their game against Olympiacos, with Zlatan Ibrahimovic opening the scoring in the seventh minute. Good news for Benfica fans.
15 minLuisao looks caught in two minds under pressure from Mitrovic but, luckily for the visitors, Artur responds well to collect the ball just inside his box.
16 minSuperb from Praet in midfield as he makes a sliding tackle to steal the ball from Perez as Benfica looked to launch an attack.
17 minSAVE! Mitrovic picks up the ball just inside the box and pulls the ball back to Bruno, whose curled effort is tipped over the crossbar.
19 minBreakthrough for the hosts! Anderlecht keep the pressure on following a corner and N'Sakala delivers a brilliant pass to Mbemba, who remained in the box to calmly slot the ball past Artur.
21 minBenfica have responded well since falling behind and it's the visitors who look dangerous again as Anderlecht are forced to clear a couple of crosses.
23 minThe visitors are struggling with the same problem they've suffered with for most of the group stage. Despite seeing plenty of the ball in advanced areas, they seem to be lacking ideas in the final third of the pitch.
25 minGaitan is furious when Kouate dives in to catch him with a late challenge. Anderlecht once again clear the danger from a set piece.
26 minAnderlecht are caught being lazy in possession and they're almost punished when Gaitan's curled pass just evades Markovic inside the box.
28 minAlmost a second for the hosts! Kouyate wins the header from a corner but Mitrovic's finish from close range doesn't count as the Benfica defence had rushed out of the six yard box.
29 minYELLOW CARD! The first booking of the match goes to Bruno for a hand ball as Benfica looked to clear. That caution rules him out of the game against Olympiacos.
31 minAnderlecht's energy has been the most impressive aspect of their game in the first half. Benfica are still enjoying more of the possession but they seem to be struggling to deal with the home team's tempo.
32 minBenfica once again to do well to leave a number of Anderlecht players in an offside position after a corner is cleared. Excellent defending.
35 minMatic pulls Benfica level as he rises highest to head home an inviting free kick from Gaitan. Anderlecht are appealing for offside but Matic was the only visiting player who had timed his run correctly. Great decision from the assistant referee.
36 minThis game is still being played at a very quick pace. Benfica will be confident now but it will be interesting to see if Anderlecht can stick to their game plan.
37 minCHANCE! Artur doesn't look brave as he comes out to attempt to collect a corner and Kouyate is inches away from making him pay when he heads just over.
39 minBenfica are seeing plenty of the ball now as they look to take the lead before the break. Lima is drifting out wide too often, meaning there is a big void in the centre of attack for the visitors.
41 minAnderlecht win the first ball from a corner once again but Bruno is punished for a push on Perez inside the box.
42 minThe noise level increases when Mitrovic breaks through on goal but an offside flag ends the striker's progress.
43 minGaitan is furious when Lima continues a poor night on a personal level with a dreadful pass towards his teammate, who had made a very good run.
45 minMarkovic chips a wonderful ball to Lima on the right side of the box but Deschacht reacts superbly to deflect the forward's effort wide. The corner that follows is easily cleared by the hosts.
8.33pmNot too much time added on at the end of an entertaining first half. Both sides are playing attacking football but neither will be happy to be level. A victory is needed tonight for both of these teams.
8.35pmPSG have reached the break in the lead in Group C's other game. Ibrahimovic's strike is making the difference in their game against Olympiacos.
8.37pmBenfica have been much stronger in possession this evening but they've struggled to create many clear opportunities. It does seem like they can improve a lot after the break.
8.40pmBoth teams enjoyed spells of superiority in the first 45 minutes but Anderlecht's pressing game could come back to haunt them if they struggle to keep up the tempo late on.
8.43pmBenfica will still be targeting a place in the knockout stages but a point tonight would secure them a spot in the Europa League.
8.45pmThe two teams are returning to the pitch now for the second half. Benfica will get the game back underway.
47 minIt's been a cagey start to the second half from both teams as the midfielders battle for control.
48 minMitrovic is convinced that Matic fouls him when both go up for a header but his complaints cost him the chance to take on Luisao.
49 minYELLOW CARD! Poor decision from the referee to book Nuytinck, who didn't make contact with a tumbling Markovic. Anderlecht easily clear the free kick that follows.
51 minBenfica are once again enjoying more of the possession as they look for the goal which would keep the pressure on Olympiacos. Anderlecht continue to frustrate the visitors with their pressing game.
53 minMbemba goes from hero to villain to hand Benfica the lead. Gaitan makes a brilliant run into the box before creating space with a clever turn. The shot might be going wide but Mbemba's deflection beats Proto. That's harsh on the hosts.
55 minSUBSTITUTION: Deschacht comes off for the hosts, with Acheampong his replacement as John van den Brom looks to attack the visitors now. N'Sakala will move to left-back.
57 minThere's still plenty of time for the home side to find a way back but it seems like that goal has given Benfica extra confidence.
59 minGreat defending from Pereira to hold off the run from Acheampong and win a free kick as the substitute looked to collect a clever header from Mitrovic.
60 minAnderlecht are sending plenty of players forward when they attack but Benfica are being gifted a lot of space on the wings. Gaitan should do better on the break but he selfishly runs through the middle and is dispossessed.
61 minSHOT! Much better play from Gaitan to pick out Lima in the box but the forward fires over with the outside of his boot from 12 yards.
63 minVan den Brom's young side have impressed this evening with their exciting brand of football but they do seem to lack quality in the final third of the pitch.
64 minNice move from the hosts as they work the ball from left to right but Bruno's cross is straight at Artur, who catches under no pressure.
65 minBenfica win a corner on the left and Gaitan's delivery finds Luisao but the defender heads well over under pressure from Mbuemba.
67 minIt's the visitors who are dictating the pace of the game now as they look to frustrate Anderlecht. Gaitan lives dangerously in midfield when he catches Nuytinck with a high challenge but there's no card issued by the referee.
69 minAnderlecht are finding their wide players with apparent ease but Benfica are doing well to deal with any cross that is delivered. Luisao, in particular, has had a very good game.
71 minSHOT! Promising signs for the hosts as they move the ball quickly in midfield to find Bruno, who fires an effort wide of the post from outside the box.
72 minSUBSTITUTION: Gaitan's job is done for the night as Miralem Sulejmani is introduced by Jorge Jesus.
73 minSUBSTITUTION: Another attacking change from the hosts, with Ronald Vargas on to replace Nuytinck.
75 minThe frustration from the home supporters is becoming obvious, despite their team's impressive display this evening.
77 minVanden Borre has started most attacks for the hosts tonight but a venture up the field has produced a big goal for the home side. A clever pass into the box finds Bruno, who keeps his composure to smash the ball home from a tight angle.
78 minYELLOW CARD! Benfica's frustration is clear as Almeida is booked for needlessly kicking the ball away.
80 minCan Anderlecht find the goal to record a big win tonight? They look the side most likely to score a winner as the game enters the final 10 minutes of normal time.
82 minAnderlecht waste a very promising position as Acheampong wastes too much time on the ball before passing to Mitrovic, who had strayed into an offside position.
83 minCHANCE! Benfica win a free kick in a very good position and Sulejmani's delivery into the box is perfect. Luisao is in plenty of space but he seems to be caught in two minds from close range as he heads wide of the target. Big opportunity missed by the visitors!
85 minUPDATE! It's just got even worse for Benfica. Kostas Manolas has just equalised for Olympiacos in Paris, so Benfica will be out of the Champions League if the score stays the same in this match.
86 minCLOSE! Superb goalkeeping from Artur to push the ball to safety from Mbemba's cross just as it looked like Acheampong would head home.
87 minCHANCE! Great opportunity for the hosts when Bruno whips in a cross but Mitrovic is up too early and he heads wide of the target.
88 minSUBSTITUTION: Rodrigo is on for Benfica to replace Perez in the closing stages.
89 minDISALLOWED GOAL! Acheampong delivers a good ball to the back post, where Mitrovic is adjudged to have fouled Luisao shortly before Mbuemba tapped in from close range.
90 minRodrigo was only given three minutes to make a difference but he's made the biggest contribution he possibly can. Sulejmani finds the substitute on the left and he sprints away before firing the ball past Proto. Benfica's qualification hopes are still alive!
90+2 minVargas steps up to take a free kick from a good position but his effort sails over the crossbar. It looks like Anderlecht are going to be beaten at home again. Artur receives a booking for time wasting.
90+4 minAnderlecht are asking questions in the closing stages but they can't find a way through as Artur collects a cross from Bruno.
9.37pmWhat a game! Both teams had their spells in this match but it's Rodrigo's late goal which earns Benfica a crucial victory. They're still playing in Paris but the good news for Benfica is that Edinson Cavani has scored in the 90th minute to give PSG a 2-1 lead.
9.38pmThat was exactly why this is the bect club competition in the world. Benfica looked like they would have to settle for a point but they've done enough to give themselves a good chance of reaching the knockout stages.
9.39pmThe final whistle has gone in Paris, which means that Benfica and Olympiacos both have seven points after five games. PSG have secured top spot, so Benfica might be more confident when they face them in a couple of weeks.
9.40pmThanks for joining me on an entertaining evening in the Champions League. Make sure you stay on the site as we bring you reaction from across Europe. Goodnight.