Sterling opened the scoring at Carrow Road inside five minutes with a sublime effort form 25 yards after seeing off challenges from two Canaries defenders before teeing up Luis Suarez for the second in the 11th minute.
Norwich hit back through Gary Hooper nine minutes into second half but Sterling was on hand to restore the two-goal advantage when pouncing on an errant pass from Bradley Johnson before advancing into the area and doubling his tally for the day.
A later goal from Robert Snodgrass had Norwich back in the hunt but fortunately for Liverpool, the damage had already been done by Sterling, who allowed them to extend their lead at the top of the Premier League table to five points.
A delighted Rodgers was full of praise for Sterling who has now scored nine league goals this term ahead of a possible World Cup call-up for the England team.
"He is arguably the best young player in European football at the moment, if he does not win the PFA Young Player of the Year this season, it is ridiculous," Rodgers said.
"I have been really pleased with his maturity, because we have tried to play him in different positions, which really tells you how intelligent he is as a footballer.
"He is a really humble kid, and it has been great to see."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball