Goals from Gary Hooper and Robert Snodgrass after halftime had Liverpool nerves jangling, but the Reds held on to clinch a massive three points in the title race.
Sterling's opener on four minutes was a beauty, beating Norwich goalkeeper John Ruddy from almost 30 metres with an arrowing drive. He then teed up Suarez with some clever approach play for the Uruguayan to poke the ball past Ruddy for Liverpool's second.
It looked like a coronation for the champions-elect. But the match turned on it's head after halftime after Hooper took advantage of some sloppy play from Reds keeper Simon Mignolet to pull a goal back.
But Sterling, with another piece of individual genius, put Liverpool 3-1 ahead eight minutes later.
However, it was still not enough and when Snodgrass converted on 77 minutes, momentum was with the hosts - and the Scot, who was outstanding in the second-half.
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