The Reds gave their top-four hopes a further boost after wonder strikes from both Jordan Henderson and Philippe Coutinho did for Manuel Pellegrini's men.
Sergio Aguero's brilliant assist led to Edin Dzeko's first-half equaliser but Brazilian Coutinho's goal was what settled matters in the second half.
And, after the win, Carragher took to Twitter to praise the goalscorers, Adam Lallana and boss Brendan Rodgers. He also singled another name out for his efforts against Manchester City.
Great game at Anfield today, Lfc outstanding particularly Coutinho, Lallana, Henderson & Allen. Rodgers deserves most credit though. #3-4-3— Jamie Carragher (@Carra23) March 1, 2015
Carragher's praise is intriguing. The Sky Sports pundit is spot on - but it makes a refreshing change for Allen's critics to have to take a step back and appreciate his value to this Liverpool side.
Against Manchester City, the Welshman was superb in midfield. But how many times has the 24-year-old let his team down this term?
Allen has received plenty of justified criticism in the past - both from neutrals and Liverpool fans alike. Here, though, he showed what he can really do.
Liverpool, meanwhile, are the absolute form team of 2015. So much so that a betting man couldn't confidently back against them sealing a Champions League place for a second right now...