Liverpool enjoyed the better of things after the break, however, and got the winning goal through Philippe Coutinho's curling strike into the top corner with 15 minutes remaining.
Here, Sports Mole takes an in-depth look at whether the Reds were worthy of their victory in a pulsating clash.
On target: 5
On target: 1
Was the result fair?
Absolutely. The match was fairly even during the opening 45 minutes, with Manchester City enjoying more of the possession but Liverpool creating the better chances. The hosts began the match slowly but soon picked up momentum and were on top when they took the lead. City's response was good, though, and they could have gone into the break ahead having seen Sergio Aguero hit the post in addition to Dzeko's goal.
The second half was a different story, with Liverpool dominating for long periods and eventually getting a deserved goal through Coutinho's spectacular strike. The Reds controlled the middle of the park, with Coutinho and Adam Lallana continually finding space in the pockets to cause City all sorts of problems. The visitors could not cope with that and eventually had to sacrifice a striker in favour of another midfielder.
That did not do much to solve the problem, however, and Liverpool maintained their control over the match on the way to a deserved victory. City had their moments and will point to that shot that hit the post, but one shot on target speaks volumes. It is their lowest tally of the campaign and, despite getting into a number of promising positions, they failed to work Simon Mignolet anywhere near as much as they should have.
There were questions over how Liverpool would cope with the fatigue element today following their defeat on penalties to Besiktas in Turkey just three days ago, but they answered those emphatically. With the exception of the first five minutes or so, the hosts played at a frenetic tempo throughout this match. They hunted the ball in packs and were quick to close City down high up the pitch, while also sweeping forward with pace when in possession.
It was the perfect response to their Europa League elimination, with their second-half display particularly impressive. It was like watching the Liverpool of last season in full flow at times, with Coutinho the conductor of wave after wave of Liverpool attacks. They dominated the midfield area and, despite a couple of shaky moments in the first half, defended well against the potent City attack too.
This, more than any other performance of the season, will raise belief amongst the fans, players and outsiders that Brendan Rodgers's side can break into the top four. They have momentum behind them and are now unbeaten in 11 Premier League matches, a run that has lifted them up to fifth in the table. If they can turn in more displays like today's then they have to be favourites for Champions League football next season.
Man City's performance
Having been humbled by Barcelona in the first leg of their Champions League clash in midweek, City made four changes to their starting XI today. However, Manuel Pellegrini persisted with the same tactics that saw his side outplayed by the Catalan giants, and once again they paid the price. Liverpool repeatedly outnumbered them in midfield and Yaya Toure and Fernandinho never got to grips with the likes of Coutinho and Lallana in behind them.
City did look dangerous going forward, particularly in the first half when David Silva began to have more of a say on the game. The midfield seemed to be functioning well going in one direction, but it was static in the other. Time after time, the visitors' back four was left exposed, and Vincent Kompany and Eliaquim Mangala struggled as a result. They were comfortably second best throughout the second half and can have no complaints at leaving Anfield with nothing.
It was another naive display from City, who are capable of blowing the lesser teams away with such tactics, but will always find it difficult against the likes of Liverpool playing like this. It caps off a disappointing week for them, with their Champions League hopes also hanging by a thread now. They could have closed the gap on Chelsea to two points today, but it remains five and City would need an incredible end to the season to avoid a trophyless campaign.
Sports Mole's man of the match
Philippe Coutinho: The outstanding player on the park today was Coutinho, who was involved in almost everything good that Liverpool did. The Brazilian had the beating of Toure and Fernandinho every time in midfield, with his influence growing as the game wore on. His passing and movement was immaculate, and he capped off a terrific display in style with a stunning winner.
This one has to go to Kompany for his role in the opening goal of the game. The City skipper lost a 50-50 challenge with Coutinho in midfield, allowing the playmaker to race forward and set up the attack that ultimately ended with Henderson thrashing the ball into the top corner.
Mark Clattenburg kept his cards in his pocket when possible today, which contributed to a free-flowing, enthralling encounter. He was a little lenient with an elbow from Wilfried Bony, but, aside from that, had a very good game in the middle.
Liverpool: Liverpool face Burnley at Anfield on Wednesday evening before a third straight home game against Blackburn Rovers in the quarter-finals of the FA Cup on Sunday.
Man City: City, meanwhile, have a couple of kind fixtures in which to bounce back from this defeat, with Leicester City next up on Wednesday before facing Burnley on Saturday.