The Uruguayan striker, who is the clear favourite to be crowned PFA player of the year, doubled the Reds' advantage on 11 minutes with a clinical side foot finish.
It looked to have put the visitors on easy street after they broke the deadlock moments earlier when Raheem Sterling sizzled a stunning 25-yard strike into the corner.
Liverpool were under the cosh but regained their two-goal advantage soon after when Sterling's dynamic run ended with a shot that looped off Bradley Johnson and over the stranded John Ruddy.
The result sees Liverpool secure an 11th straight win and moves them five points clear of second-placed Chelsea ahead of next Sunday's showdown between the two sides at Anfield.
PRE-MATCH: No Sturridge for Liverpool: Daniel Sturridge is not risked by Rodgers as he makes two enforced changes from the win over Man City. Lucas and Allen replace the England striker and the suspended Henderson. As for Norwich, Adams makes one change to the team that lost at Fulham with Hooper coming in for van Wolfswinkel in attack.
4' - GOAL: Norwich 0-1 Liverpool. Raheem Sterling picks up the ball off Suarez and jinks past his man before hammering a shot into the corner. Fantastic start for Liverpool.
11' - GOAL! Norwich 0-2 Liverpool. It's that man Suarez once again. Sterling breaks free down the left and tucks a delightful low pass into Suarez who coolly side foots into the corner. Liverpool on fire once more as their number 7 makes it 30 for the season.
17' - NORWICH CHANCE. Redmond launches a free kick into the mix that is only half cleared by the visitors. A ball from the right drops to Hooper but he can't get clear of a sea of red shirts and his shot is somehow blocked. Almost a goal back for the hosts!
54' - GOAL! Norwich 1-2 Liverpool. Norwich are back in it! A quick throw catches Liverpool out and when the right-wing cross came in, Mignolet flapped under pressure from Bradley Johnson, allowing Hooper to slot into an empty net. Game on!
62' - GOAL! Norwich 1-3 Liverpool. Liverpool regain their two goal advantage. A mistake by Bradley Johnson gifts the ball to Sterling who rampages at goal and then drills in a shot that takes a big deflection off the defender and loops over Ruddy.
77' GOAL! Norwich 2-3 Liverpool. Olsson hangs a cross up towards Snodgrass who rises above Flanagan to guide a header into the corner. 2-3 and nervy moments for the Reds.
83' NORWICH CHANCE! Glen Johnson loses possession and Norwich come again... a corner is worked short to Olsson who arrows in another cross for van Wolfswinkel who sees his header well saved by Mignolet. Breathtaking stuff out there.
Luis Suarez is only the second player to reach 30 PL goals without a single penalty in the total (Andy Cole also achieved it with 34 goals in 1993-94).
The last time a Liverpool player scored 30 league goals in a season (Rush 1986-87), Neil Adams won the title (with Everton).
Liverpool have now scored 57 first half goals in the Premier League this season, one more than Man Utd have in total currently.
Liverpool have won 11 games in succession within a single season for only the second time in their top-flight history (They also did it in May 1982).
Norwich have now conceded more Premier League home goals than Liverpool (15) this season.
(Stats courtesy of Opta Joe)
TALKING POINT: Is the title now destined for Anfield? After Chelsea's shock loss to Sunderland on Saturday night, the focus shifted to the Merseysiders to see if they could take advantage and hold their nerve. They continued their fine form and are now clear favourites to land a first ever Premier League crown. Next weekend they face Chelsea at Anfield with Man City still lurking in the shadows. But there's no doubt it is Liverpool's to lose at this point.
MAN OF THE MATCH
Raheem Sterling (Liverpool): Sterling has been one of the stars of Liverpool's season and continued his scintillating form with two goals and an assist. In the absence of Sturridge he forged a new-look SAS with Suarez that did enough to see off Norwich and keep Liverpool on course for the title.
Norwich City: Ruddy 7, Whittaker 6, Martin 6, Turner 6, Olsson 7, Johnson 6, Howson 6, Fer 6, Snodgrass 7, Redmond 7, Hooper 7. Subs: van Wolfswinkel 6, Murphy 6.
Liverpool: Mignolet 5, Johnson 6, Skrtel 7, Sakho 5, Flanagan 6, Gerrard 6, Lucas 6, Allen 7, Sterling 8, Coutinho 6, Suarez 7. Subs: Moses 6, Agger 6.
THE MATCH IN TWEET
- Sports & Recreation
- Raheem Sterling
- Premier League
- Luis Suarez
- Simon Mignolet
- Gary Hooper