Liverpool beat second placed Manchester City 2-1 at Anfield to move into fifth place in the Premier League.
Jordan Henderson opened the scoring on 11 minutes but Aguerro setup Edin Dzeko with a wonderful assist for the equaliser soon after.
The scores remained level until 75 minutes when Coutinho scored another wonder goal to give Liverpool the lead.
Liverpool head coach Brendan Rodgers decided to start with Emre Can in defence against Manchester City after playing the 21-year-old in a midfield role against Beşiktaş in the Europa League Round of 32.
The Reds are yet to lose a Premier League game in which Emre Can has started in defence.
The 21-year-old has started in Liverpool’s last nine league games as a defender.
Liverpool take on Burnley next at Anfield while Manchester City take on last placed Leicester City.
Liverpool: Mignolet, Can, Skrtel, Lovren, Henderson, Allen, Moreno, Markovic, Lallana, Coutinho, Sterling
Subs: Ward, Toure, Lambert, Sturridge, Borini, Balotelli, Williams
Manchester City Hart, Zabaleta, Mangala, Kompany, Kolarov, Fernandinho, Yaya Toure, Silva, Nasri, Dzeko, Aguero.
Subs: Caballero, Demichelis, Clichy, Lampard, Bony, Milner, Fernand
Goals: 11′ Henderson, 25′ Dzeko, 75′ Coutinho