Sterling restored his side's two-goal lead just after the hour, while Robert Snodgrass netted on 77 minutes to set up a nervy finale.
Read Sports Mole's minute-by-minute report below to find out how all of the action unfolded between the two teams.
11amHello there and welcome to Sports Mole's live text coverage of this afternoon's early kickoff in the Premier League as Norwich City welcome Liverpool to Carrow Road. We should have some team news through for you shortly.
11.05amLiverpool boss Brendan Rodgers makes two changes to his starting XI following last weekend's 3-2 win over Manchester City. Daniel Sturridge has failed to recover from a hamstring strain and misses out on a place in the squad, while Jordan Henderson starts his three-game ban. Joe Allen and Lucas Leiva are the players who come in.
11.08amNORWICH SUBS: Bunn, van Wolfswinkel, Gutierrez, Garrido, R Bennett, Tettey, J Murphy
11.10amNorwich caretaker boss Neil Adams opts to make just the one change after last weekend's 1-0 defeat to fellow strugglers Fulham as Gary Hooper replaces Ricky van Wolfswinkel up front.
11.13amRight, down to business. Today's match could prove to be absolutely huge at both ends of the table, shaping the title race and the relegation battle. A win for Liverpool this afternoon would send the Reds a commanding five points clear of second-place Chelsea following the Blues' surprise 2-1 defeat at home to Sunderland yesterday. A victory for Norwich would see the Canaries climb five points clear of the drop zone.
11.16amIt's hard to look beyond anything other than a Liverpool win at Carrow Road due to their immense success against the Canaries in recent season. However, Sunderland's incredible victory at Chelsea on Saturday should give Norwich some confidence coming into this match.
11.23amLiverpool are the Premier League's in-form team at the moment, winning their last 10 matches in a row. They've also gone unbeaten in their last 15 games. Whichever way you look at it, that's title-winning form. Meanwhile, Norwich start the day on the back of three consecutive defeats.
11.27amLiverpool captain Steven Gerrard recently speaking to PA Sport: "We have to treat Norwich like we treated AC Milan in 2005. We have to forget what colour their kit is and the personnel wearing it and treat them as the best players in the world.
"We have to forget where we are and forget what we've done. We have to prepare for Norwich like it's the last game of our careers. Every game is going to get bigger and bigger because we are getting close to that last game of the season.
"Of course Man City was always going to be huge at Anfield because they are in the race with us but Norwich now become Man City, Norwich now become Chelsea, Manchester United - that's how big it is."
11.30amNorwich caretaker boss Neil Adam speaking to the club's official website: "It speaks for itself their run, and we respect that, but all runs are due to come to an end at some time and why can't it be theirs that comes to an end at Carrow Road on Sunday?
"It's going to be tough, of course it is, but we're confident. We treat every team the same. The research has been thorough, and we've spotted one or two weaknesses and identified one or two areas where we think we can have a little bit of joy against Liverpool."
11.33amHEAD TO HEAD: The history books regarding this fixture do not make good reading for Norwich City, particularly in recent years. Liverpool have the better overall record with 29 wins compared to the Canaries' 11. The teams have also played out 11 draws.
11.35amLiverpool have not been beaten in nine matches by Norwich, with the last four games going the way of the Merseysiders. During those four games they have scored a whopping 18 goals. They've found the net five times in each of their last three encounters against the Canaries.
11.39amAs you can see from the stat below, Luis Suarez has given Norwich an absolutely torrid time in recent years. The Uruguayan seems to relish playing against the Canaries, scoring all manner of goals. Two long-range specials spring to mind when thinking about Suarez and Norwich, including a spectacular effort during the Reds' 5-1 win at Anfield earlier this season.
11.42amREFEREE WATCH: Today's referee is Andre Marriner, who has handed out 69 yellow cards and seven red cards (sometimes for the right player) this season.
11.45amGoing back to the head-to-head record between these teams, the last time that Norwich beat Liverpool was a 1-0 win at Anfield in 1994. They're going to have to be at the top of their game to repeat that this afternoon, but three points would be a huge boost in their bid to stay in the top flight.
11.47amWith just under 15 minutes to go until kickoff, you should have enough time to pore over Sports Mole's preview of this afternoon's match at Carrow Road.
11.50amPREDICTION TIME: As mentioned earlier, only a brave person would bet against Liverpool winning this match. The Reds have been imperious over the last few weeks and are fully deserving of their place at the top of the table. Much has been made of whether they will be able to cope with the pressure heading into the final few weeks of the season, but we here at Sports Mole can see them earning a comfortable 4-1 victory over a Norwich side that is struggling for inspiration.
11.56amThe players are in the tunnel, ready to walk out onto the pitch at Carrow Road. The travelling Liverpool fans are making plenty of noise in their corner of the ground. Not long to go now until this crucial match gets underway.
1 minKICKOFF! The teams are out, the pre-match handshakes have been done, and it will be Norwich to kick us off at Carrow Road. Here we go!
3 minWHAT A GOAL FROM RAHEEM STERLING! The youngster received the ball about 25 yards from goal before firing an unstoppable drive past Ruddy and into the top corner. That was an incredible strike from the winger. Liverpool make the breakthrough with just three minutes on the clock.
6 minThat goal aside, Liverpool have started this match very positively indeed. They've been completely in control of the ball, while Norwich have struggled to gain possession. It looks like it could be a long afternoon for the Canaries.
9 minSAVE! Almost a second goal for Liverpool, who are looking rampant. Allen was played in down the right, but his effort on the angle was parried away by Ruddy. The Norwich goalkeeper really had to be on his toes there because that strike was hit venomously.
10 minWho else? Luis Suarez doubles Liverpool's lead with a clinical strike that saw Sterling play a big part. Sterling made a good run down the left before sliding a wonderful cross in towards the striker, who slotted past Ruddy with a cool first time finish. Is this game already over?!
15 minNorwich are all over the place at the moment. They are making a right mess of it when they're in possession, and they can't handle Liverpool when the visitors go forward. The hosts need to forget about getting themselves back into this game with a goal. The best thing that they can do is to keep it tight at the back and keep the score as it is for now.
16 minCHANCE! Close for Norwich as they mount a rare attack! The ball bobbled around in the box from a corner, allowing Hooper to get a shot away. However, Allen was there to block the striker's effort. Fer then tried to squeeze the ball in, but he was crowded out by the Liverpool defence.
19 minThat opportunity for Hooper seems to have given the hosts a bit more confidence. They're not showing any fear when it comes to having a crack at goal, as Whitaker just demonstrated with a long-range drive that was blocked by Skrtel.
22 minNeil Adams is sure to be encouraged by what he's seeing from his players at the moment. Norwich are putting up much more of a fight now, particularly in midfield. Liverpool have been limited to the odd counter-attack in the last few minutes.
25 minLiverpool aren't providing much of an attacking threat right now, but they don't look too flustered by Norwich. The visitors are happy to remain patient and build from the back. The match has certainly settled down following that frantic opening 10 minutes.
26 minCHANCE! That could easily have been 3-0 for Liverpool through Allen, but the midfielder can only flash his shot narrowly wide from 25 yards. That was a decent strike from the Welshman, who looks like he fancies a goal this afternoon.
28 minYELLOW CARD! That's as clear a booking as you're likely to see this season. Snodgrass is the player who's cautioned after sliding in late on Allen. That was a poor challenge from the Norwich midfielder.
31 minCHANCE! A decent opening for Norwich there with Sakho dispossessed by Howson, who lays the ball off to Snodgrass. The Scot tries to find Hooper at the back post, but Skrtel cuts out his cross. Norwich are starting to build some momentum.
34 minThere's a fascinating ebb and flow to this match right now. Both teams are showing plenty of attacking intent, though it's Norwich who are continuing to look more likely to get the next goal. What a boost it would be for them if they could find the net before the half-time whistle.
37 minIt's an uncharacteristic game that Liverpool have been playing these last few minutes. They've been making a number of errors, which is very unlike them indeed. However, Norwich have failed to capitalise. The hosts are lacking that killer touch in front of goal.
40 minFive minutes of normal time left to play in this first half at Carrow Road, and the game has gone decidedly flat. Liverpool are sure to be pleased with their 2-0 advantage, but another goal would do them nicely. As it stands, Norwich still have a chance to get something out of this.
43 minLiverpool are slowing the pace down now as we head towards the final few minutes of the half. The Reds are passing the ball around at a leisurely pace, making Norwich do all of the running.
44 minYELLOW CARD! Norwich defender Turner is the latest name to go into the book for bringing down Sterling with Liverpool on the break.
45 minThere will be two minutes of added time at the end of the half...
12.49pmAndre Marriner blows the half-time whistle, bringing an end to a successful 45 minutes for Liverpool. The Reds lead Norwich 2-0 thanks to early goals from Raheem Sterling and Luis Suarez. The Merseysiders will move five points clear at the top of the table if things stay the same.
12.52pmAs for Norwich, a poor start has cost them in this match. The Canaries struggled to contain Liverpool early on, but it must be said that they have improved since then. It's a long way back for them, though they have shown one or two encouraging signs.
12.58pmThere's definitely a way back into this match for Norwich, but they're going to have to improve dramatically up front. Creating chances hasn't been their biggest problem. Instead, it's a lack of finishing that has troubled them.
13.01pmWhile Norwich will need to attack Liverpool during the second half, a third goal for the visitors would surely kill the game off. There were some question marks over whether they would miss Daniel Sturridge today, but they have done perfectly well without him.
46 minSECOND HALF UNDERWAY! The teams are back out, and it will be Liverpool to kick off the second half. No changes for either side at the break.
48 minCHANCE! Liverpool come close to adding a third early in the second half as Suarez's glorious pass finds Coutinho, who then picks out Sterling on the edge of the box. The winger hits it first time, but he can only guide the ball over the crossbar. Clinical stuff from the visitors.
51 minIt's been a live start to the second period from both teams. Norwich are certainly giving it a go. An earlier corner for the hosts is easily gathered by Mignolet, while a second is hacked away by the Liverpool defence.
53 minIt's been coming! Norwich are level as Gary Hooper taps in from close range following poor judgement from Mignolet. The Liverpool goalkeeper got nowhere near a cross from the right, allowing the Norwich striker to slot into an empty net. That goal has changed the whole atmosphere inside Carrow Road.
56 minCHANCE! Almost an instant response from Liverpool as Suarez tricks his way through the Norwich defence, but the Uruguayan sees his shot on the angle saved by Ruddy. It's end-to-end stuff at the moment.
59 minCHANCE! Inches away for Suarez and Liverpool! Yet again the striker bobbed and weaved inside the Norwich box before curling a shot narrowly wide of the far post. The home side are going to have to ride their luck a bit if they want to stay in this game as Liverpool will continue to pose a threat up front.
61 minCould that be the killer blow in this match? Raheem Sterling makes it 3-1 to Liverpool, though that goal had a huge slice of luck to it. The winger made a great run from his own half before seeing his effort deflect off a Norwich defender and over the head of Ruddy.
64 minNorwich REALLY have to go for it now if they want to take something from this game. Meanwhile, Martin Skrtel goes into the book for bringing down Nathan Redmond.
67 minThat goal has really knocked the stuffing out of the Norwich fans and players. They were forcing the issue up until Sterling found the net. That said, another goal in the next 10 minutes could give them some hope. Snodgrass tries his luck from distance, but Mignolet is equal to it.
71 minCHANCES! A couple of good opportunities for Norwich there. The first sees Redmond's long-range effort deflected narrowly wide by Skrtel. Martin then heads over the resulting corner when he really should have got the ball on target.
72 minYELLOW CARD! Norwich's Jonny Howson now goes into the book for a foul on Sterling. Just under 20 minutes left for the hosts to get something out of this game.
75 minLiverpool are trying to take the sting out of this game at the moment, by nudging the ball around and making Norwich work hard for it. The Canaries are still chasing around with plenty of enthusiasm, but they're finding it tough to trouble their opponents.
76 minSUBSTITUTION: Liverpool make their first change of the afternoon as Victor Moses enters the action in place of Philippe Coutinho.
77 minNow then! Norwich give themselves a lifeline with just over 10 minutes left to play as Robert Snodgrass heads in brilliantly following a cross from the left. Can the Canaries salvage something from this game? They make two changes in the wake of that goal, with Fer and Hooper being replaced by Murphy and Van Wolfswinkel. Flanagan also goes into the book for barging over Snodgrass.
80 minSUBSTITUTION: Another change for Liverpool here as Daniel Agger replaces Joe Allen.
82 minCHANCE! It should be 3-3! A cross from the left is met by the head of Van Wolfswinkel, but the striker can only direct his effort straight at Mignolet. Anywhere else and it would have been a goal.
85 minFive minutes left to play at Carrow Road, and it's Norwich who are doing all of the pressing. They're pushing everyone forward in search of what would be a hugely-important equaliser in their quest for Premier League survival.
88 minHas time run out for Norwich? They really haven't got long left to get something out of this match, but the chances seem to have dried up for them. Liverpool are doing well to hang on.
1.54pmThe full-time whistle goes, meaning that Liverpool are now five points clear at the top of the table with just three games left to play! The Reds had to work hard for it as Norwich were really piling on the pressure towards the end there, but they managed to hold on for what is a vital win.
1.56pmNorwich gave their all during the match, but it was not enough to stop them slipping to a fourth consecutive defeat. The Canaries remain two points clear of the relegation zone with three games remaining.
1.58pmThat's all from our live text coverage of this afternoon's game, but don't forget that you can keep up to date with all of the post-match reaction right here on Sports Mole. Thanks for your company, and we hope to see you again soon. Goodbye!