The 17-year-old scored his first competitive goal for the club to give Brendan Rodgers a league victory at Anfield at the fifth attempt.
The result elevates the Reds into mid-table with eight games played as they prepare for tough fixtures against Everton, Newcastle and Chelsea.
The only change for Liverpool from their goalless draw with Stoke was an enforced one, Brad Jones replacing the injured Pepe Reina to make his first Barclays Premier League start for the Reds.
The hosts were quick to establish their dominance against a side that had conceded 14 goals in seven games heading to Anfield.
Nuri Sahin attempted a dipping effort from the angle of the box on the quarter-hour mark and Sterling bent one from 20 yards, though goalkeeper Alex McCarthy wasn't overly troubled by either.
Jones, a spectator for most of the first half, collected a cross and bowled quickly into midfield, where Luis Suarez and Steven Gerrard seized possession before dispatching Sterling down the left. The 17-year-old might have had too much time to ponder, for his decision to stall and try to beat a man led only to a goal kick.
Full report: Liverpool FC Official
Source: FootyTube
Meanwhile, Dalglish has been busy selling off spare parts, as he tries to negotiate deals for everyone from Alberto Aquilani and Raul Meireles to Jay Spearing and David Ngog. 
