Sterling restored his side's two-goal advantage just after the hour, while Robert Snodgrass netted on 77 minutes to set up a nervy finale.
Here, Sports Mole takes a closer look at the action between the two teams at Carrow Road.
On target: 5
On target: 6
Was the result fair?
While Norwich made Liverpool sweat towards the end of the match, Brendan Rodgers's side were the deserved winners in the end. The Reds were more clinical up front and did what was necessary to get over the line. The mark of champions.
Norwich can take a lot of pride from the fact that they pushed Liverpool until the final whistle. The Canaries were not helped by conceding two early goals, but after that it was a case of the hosts knuckling down and refusing to give up. They played with a fierce and intense tempo, particularly in midfield, and used the pitch well to stretch their opponents. A bit more composure would not have gone amiss, though this is only a minor quibble on what was an otherwise encouraging afternoon. A few more displays like this and they are likely to be okay for another season.
The Reds had to ride their luck at times, but they managed to seal the points thanks to some ruthless finishing and a grittiness that all teams need when challenging for the title. Their task was made a lot easier by scoring two goals inside the opening 11 minutes, although after that they did not always have things their own way. They were their usual selves in attack, breaking with pace and frightening the life out of their opponents with their dynamic play. However, once again they showed that they are vulnerable in defence. But forget all of that: with only three games left to play, only a brave soul would bet against them clinching their first title in 24 years.
Sports Mole's man of the match
Raheem Sterling: The Liverpool winger was in devastating form at Carrow Road, running at the Norwich defence whenever he could with his trademark pace and directness. His first goal was a sensational strike from long range, while the second saw him rewarded with a bit of luck following a superb run. Looking further ahead, the 19-year-old could be England's secret weapon at this summer's World Cup.
Simon Mignolet made a bad error for Norwich's opening goal, getting nowhere near a cross to allow Gary Hooper the opportunity to slot the ball into an empty net. It did not cost his side in the end, but it certainly gave the hosts some impetus when they were struggling.
Andre Marriner could have been a bit more generous to Norwich when it came to one or two decisions, although the official had a decent enough game out in the middle during what was a crucial encounter for both teams.
Norwich: The Canaries continue their bid for Premier League survival on Saturday when they travel to Manchester United.
Liverpool: The Reds can take a step closer to clinching the Premier League title next Sunday when rivals Chelsea make the trip to Anfield.