The French champions had already brushed aside Olympiacos and Benfica to move to the top of Group C, while Anderlecht had lost both their opening matches in the competition and were rooted to the bottom of the pool without a point.
However, the trend continued as PSG smashed their way past the Belgian outfit at Constant Vanden Stock.
Read how the match unfolded in our live commentary below.
6.51pmTonight should be another fabulous night in Europe's elite competition, and our attention is in Belgium for what is already a 'must-win' game in Group C.
6.54pmHosts Anderlecht have had a shocker so far. They have lost against both Benfica and Olympiacos in their opening two matches and will not be feeling too confident heading into this clash against the group favourites. They'll feel that they have to get something from this match before they fall too far behind the other teams in the pool.
6.58pmMeanwhile, PSG are flying. They have cruised to comfortable wins in their opening two games and now have their place at the top of Ligue 1 back following the weekend's action. Laurent Blanc's side are still yet to taste defeat this season, so Anderlecht have a real job on their hands here.
7.01pmI'll bring you more on their current form shortly, but first, here are the teams.
7.13pmPSG XI: Sirigu, Van der Wiel, Marquinhos, Alex, Maxwell, Motta, Verratti, Matuidi, Cavani, Lavezzi, Ibrahimovic
7.15pmLaurent Blanc has opted to make a staggering six changes to his team, following their 4-0 triumph over Bastia at the weekend.
7.17pmLucas Digne, Christophe Jallet, Lucas, Jeremy Menez, Adrien Rabiot and Hervin Ongenda have all dropped out of the team having started in Ligue 1 on Saturday.
7.18pmFor this match, Blanc has drafted in Gregory van der Wiel, Maxwell, Thiago Motta, Marco Verratti, Ezequiel Lavezzi and Edinson Cavani.
7.21pmSo a lot of changes for Les Parisiens from their last outing, but this is probably the strongest team available to Laurent Blanc minus the absence of captain Thiago Silva. Van der Wiel and Maxwell come in as the full-backs while Verratti and Motta take up their usual spots in the centre of midfield.
7.23pmIt will be interesting to see what Blanc does to his PSG attack tonight. He will either opt for four in midfield and place Matuidi and Lavezzi out wide with Cavani partnering Ibrahimovic up front. Or he could go for a 4-3-3 and leave Matuidi in the midfield trio and place Cavani and Lavezzi on the flanks, either side of Ibrahimovic.
7.33pmSo how have both these teams fared so far this season? Well, Anderlecht have lost four out of their 11 league games already this term, despite being crowned as the champions last year. They sit fifth in the table, seven points behind the league leaders.
7.35pmMeanwhile, PSG have picked up from where they left off last season. Only this weekend did they move to the top of Ligue 1 following AS Monaco's draw. However, they are now two points clear as they look to retain their crown and are still unbeaten in all competitions.
7.38pmIt may seem hard to believe seeing as that they've both competed at the top of Europe for so long, but this is actually the first time that these two sides will meet in their history.
7.45pmThe teams are both out. Anderlecht wearing their all-purple home kit, PSG sporting their all-white with blue and red away strip.
1 minKICK OFF! PSG, playing from right to left in this first half, get us underway.
4 minNo real chances for either side yet. Ibrahimovic was just chipped in over the top to go one on one with the goalkeeper, but he was flagged offside. Even in terms of early possession.
5 minDecent cross into the box from the left win by Suarez, who is Anderlecht's top scorer so far this season, and Mitrovic gets above Marquinhos to head the ball at goal, but it's comfortably caught by Sirigu.
7 minAnderlecht certainly aren't showing any signs of fear in these opening exchanges. They are happy to try to take the game to the group favourites.
8 minSAVE! What was I saying? Suarez picks the ball up slightly left of centre from about 25 yards out and takes a touch before firing a low effort towards the bottom corner. Sirigu is slowly across and puts the ball behind for a corner.
12 minMISS! Ibrahimovic beats the offside trap and is through on goal. He loses his bearings of where he is as the ball bounces down towards him and he eventually takes it past Kaminski wide. But he can only slot wide of the near post from an acute angle.
13 minIt may not have been the easiest of chance for Ibrahimovic, but he will have hoped to have done better. It was a terrific past from Verratti.
17 minGOAL! Anderlecht 0-1 Paris Saint-Germain (Zlatan Ibrahimovic)
17 minIt has looked to have been coming over the past few minutes but PSG take the lead. Van der Wiel makes a run down the right side of a crowded box before being found by Cavani and then picks out Ibrahimovic with a low pass across the face of goal which the skipper cannot miss.
19 minIt's been a decent response from the hosts, who are trying to get at PSG as much as they can.
20 minSAVE! Nealy 2-0 for PSG as a nice passing move forward ends with a deflected shot inside the box from Van der Wiel, but Kaminski is there to push the ball behind his left post.
22 minGOAL! Anderlecht 0-2 Paris Saint-Germain (Zlatan Ibrahimovic)
22 minIt's the same combination for PSG, but it's a genius finish from Ibrahimovic. Van der Wiel plays a low cross from the right touchline into the near post, where Ibrahimovic lets the ball roll through his legs before finding the net with his right heel. Brilliant.
25 minAnd already, this game looks to be over. Ibrahimovic is in top form at the moment, and PSG now look to have really taken the wind out of Anderlecht's sails.
28 minIt's all PSG now, Anderlecht don't seem to know what to do. The away side are just leisurely knocking the ball about. The pace of this match has slowed down in recent minutes.
30 minIt's nearly the same frightening combination again as Van der Wiel is threaded through down the right. He looks for Ibrahimovic once again at the near post, but this time the ball is put behind.
33 minIbrahimovic is really in the mood tonight. He is just shrugging his markers off the ball and is pulling off some wonderful little flicks to play in his teammates.
36 minGOAL! Anderlecht 0-3 Paris Saint-Germain (Zlatan Ibrahimovic)
36 minIncredible, just incredible. Ibrahimovic has the whole crowd applauding him as he completes his hattrick. The PSG attack down the left is cleared, but only as far as Ibrahimovic. He smashes the ball first time on the half-volley from more than 30 yards out and it flies fiercely into the top corner. It's a stunning goal and a brilliant hattrick.
38 minAmazingly, that is Ibrahimovic's first Champions League hattrick. What a way to get it.
43 minThe match has hit a lull where it seems that both sides are still in awe of Ibrahimovic's class. Anderlecht, to their credit, are still keen to create chances, but PSG are standing very resolutely at the back.
45 minTielemans curls the ball in from the corner on the right, but for the third time this match Ibrahimovic is able to clear it away at the near post.
45 minHALF TIME: Anderlecht 0-3 Paris Saint-Germain
8.32pmThat should really read: Anderlecht 0-3 Zlatan Ibrahimovic. He has been simply out of this world with three outstanding goals to his name and the final one being an absolute belter to complete his hattrick.
8.33pmNot only has he been lethal in front of goal, but it's all over the pitch as well. PSG have already won this match, and look as if they have one foot already in the knockout stages.
8.44pmThe players are making their way back onto the field, and there looks as if there is going to be a substitution.
8.45pmANDERLECHT CHANGE Surprisingly, it's Matias Suarez who has been taken off by the hosts, with Acheampong coming on.
46 minKICK OFF! Anderlecht, playing from right to left, get the match back underway.
47 minDecent start to the half from Anderlecht as they win two straight corners, but nothing comes of them.
48 minSAVE! Sirigu nearly gifts Anderlecht a goal as he passes the ball straight to Gillet on the edge of the box, who hits a shot first time. However, Sirigu can just get across his line in time to hold the effort.
52 minGOAL! Anderlecht 0-4 Paris Saint-Germain (Edinson Cavani)
52 minThis is very unlucky for Anderlecht and for the right-back Mbemba. He has the ball on the edge of the box but slips over, which allows Matuidi to cross to Cavani for a tap-in.
53 minYELLOW CARD N'Sakala brings down Cavani on the edge of the box for a free kick.
54 minSAVE! Kaminski is nearly knocked off his feet following Ibrahimovic's hammer shot, but he manages to stay strong and clear.
56 minPSG CHANGE Straight swap in defence as Camara comes on for Alex.
58 minJust for the record, Ibrahimovic's third goal was clocked at 62mph. That's staggering.
59 minAnderlecht had the ball in the back of the net, but Mitrovic had already been penalised for smashing into Sirigu.
61 minSAVE! Cavani nearly has a second after running onto a long ball and tries to lob Kaminski, but it's saved by the keeper.
62 minGOAL! Anderlecht 0-5 Paris Saint-Germain (Zlatan Ibrahimovic)
62 minThis is unreal. Ibrahimovic has his fourth and PSG's fifth. He brings a ball over the top under control on the right of the box before smashing a shot on the bounce into the bottom far corner off the post. Amazing stuff from the big Swede.
63 minPSG CHANGE Rabiot is on in midfield for Matuidi.
67 minTo put into context his recent hot streak. Ibrahimovic now has 10 goals in his last five games.
69 minPSG nearly find a way through again as Lavezzi finds room down the left. Cavani and Ibrahimovic both have space in the middle, but he messes up the pass and is furious with himself.
71 minPSG CHANGE Final swap for the away side as Lucas comes on for Lavezzi.
72 minANDERLECHT CHANGES Mitrovic and Praet are replaced by Cyriac and Milivojevic.
74 minSAVE! Wonderful reaction stop from Sirigu, who claws the ball out of the sky following a massively deflected shot.
76 minCLOSE! Ibrahimovic brings the ball down brilliantly on the edge of the box from a Verratti pass but is forced wide by Kaminski. He looks as if he is going to wait for support, but instead has the guts to chip it at goal but it lands on top of the netting. It was not far off.
77 minI must say, Verratti has been brilliant this evening both with and without the ball.
82 minAll PSG still, and they still look as if they want to add to their goal tally. Both teams still attacking.
86 minCLOSE! Huge credit to Kaminski, who makes a double save from Ibrahimovic inside the box and has to be brave when chasing down the second effort. He takes a whack from the big man in the process.
89 minSAVE! Great effort from Cyriac, who wiggles free on the edge of the box before thumping a shot at goal, but Sirigu can make the stop.