Liverpool's rested duo Jordan Henderson and Philippe Coutinho score the goals to keep the reds in the hunt for a top four finish.
Thursday night's defeat in Istanbul ended the hopes of any European silverware but the team bounced back to continue their good home record against Man City.
Henderson, Markovic and Coutinho all returned to the side - with Emre Can dropping back into defence. Daniel Sturridge and Mario Balotelli both started against Besiktas, but here they both began the game on the substitutes bench - with Raheem Sterling leading the attacking line.
In the 11th minute Coutinho snapped the ball away from Kompany, before Sterling slid the ball to Henderson who curled his shot beautifully into the net.
At the other end Aguero saw a shot rebound off the post before he created City's equaliser - his pass found Dzeko in the 25th minute who fired past Mignolet.
Liverpool were showing few signs of tiredness from mid-week although Coutinho appeared to have benefitted from the break. He was likely to be the match-winner and in the 75th minute he collected the ball and fired the ball into the goal in front of the Kop.
The reds move up into 5th, taking advantage of Southampton's defeat yesterday and Liverpool have now won 26 out of the last 30 points in the Premier League - a massive improvement on the awful opening league form.