Sterling scored the opening goal with a wonderful strike in the fourth minute before turning provider for Luis Suarez to double the visitors advantage in the 11th minute.
Sterling then capped a memorable display with a deflected finish after a mazy counter-attacking run and his performance had Rodgers purring.
“I think he’s the best young player in European football at the moment.” Rodgers told Sky Sports. “At 19 years of age I don’t see anyone better.
“His intelligence with the ball, his movement and obviously he’s been concentrating on his goals.
“His first goal was a wonderful strike. He’s just shifted it and got his shot off and to beat a goalkeeper of John Ruddy’s quality shows you the level of the strike.
“His pass for Luis’ (Suarez) goal was like a midfield player. A top pass and Luis guided it in really well so there’s an assist.
“His positioning for the counter attack when he broke away. He gets a little bit of luck on the deflection but his overall performance, he’s shown so much maturity. And as I’ve said, for me he’s the best young player in Europe at the moment.”
Liverpool started quickly and were 2-0 up before the Canaries had chance to take stock.
However, they were twice pegged back by a resilient Norwich team who are in the midst of their own battle to avoid relegation.
First Gary Hooper pulled a goal back to make it 2-1 and after Sterling’s second Robert Snodgrass nodded in to make it 3-2 as the Reds had to endure yet another nervy finish.
Rodgers side have now scored at least three goals in 20 of their 35 league games this year and the 41-year-old admitted his free-scoring side have their sights set on the 100 goal barrier.
“The most important thing was to get three points and also the performance level. We are on 96 goals now and our idea is to get 100 plus – that would be an incredible effort,” he said.
Liverpool are guaranteed a place in next season’s Champions League which, given their hopes at the start of the season, is testament to what a phenomenal job Rodgers has done irrelevant of whether they can win the title.
“The objective at the start of the season was to qualify for the Champions League – that was always going to be an incredible task but now we know we cannot finish lower than third.
“We will go into the next three games looking to perform well. We want to continue to fight and now look to Chelsea next week – where it will be an incredible atmosphere at Anfield.”
(Reporting By Tom Hayward, editing by Pritha Sarkar)