The defeat was Newcastle’s fifth in succession and means they are still not yet completely out of relegation danger, while Liverpool are back within four points of the top four.
Sterling scored a superb opener for Liverpool in a game they totally dominated. He brilliantly controlled a crossfield pass from Jordan Henderson and cut inside to glide past Ryan Taylor and Gabriel Obertan and clip a shot over Tim Krul.
Liverpool could have been out of sight inside the first half hour as Alberto Moreno burst forward and tested Krul from out wide and Coutinho beat the defence only to err with his final ball. Sterling shot at Krul and when Coutinho found Henderson with a nifty backheel it seemed Liverpool were in complete control.
But Newcastle, who had appeared jaded after their recent losses, found some life before the break. Mehdi Abeid first brought Simon Mignolet into the game with a shot from the edge of the area and Liverpool appeared to have been caught out when Dejan Lovren felled Ayoze Perez in the area.
Perez was denied again before the break, this time by a brilliant save from Mignolet, after directing a header towards the top corner. Abeid spurned another good opportunity when he shot over but Liverpool regrouped. They should have doubled their lead just before the hour after Henderson broke down the right and Taylor failed to cut out his pass but Sterling somehow put a gilt-edged chance wide.
Liverpool cranked up the pressure and their second came after more poor defending from the visitors on 69 minutes. This time Mike Williamson failed to deal with a ball into the area and Allen lashed home from close range. Things began to get worse for Newcastle as Sissoko became embroiled in a needless argument with Glen Johnson and both players were booked for pushing and shoving.
Sissoko was then given his marching orders just five minutes later after a poor challenge on Lucas which could easily have warranted a straight red card rather than a second yellow. Sterling might have made the win even more comfortable six minutes from time but blazed over when well placed.