It took Brendan Rodgers's side less than four minutes to go in front. Raheem Sterling sidestepped past Robert Snodgrass and unleashed a stinging drive that flicked off Michael Turner before rippling the corner of the net.
© Getty Images
This time Sterling was the creator, weighting a low cross perfectly into the path of Luis Suarez, who opened his body to tuck home league goal number 30 for the season.
Norwich almost halved the deficit just after the quarter-hour mark when the ball dropped Gary Hooper's way in the area, but he couldn't squeeze off a shot.
Just before half time, Coutinho almost made it three when his curling shot from the left of the area flashed a yard wide of the far post.
Follow the second half live on Sports Mole by clicking here.