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Guardiola’s men recovered though and were 2-1 up heading into half-time thanks to Phil Foden and Rodri’s strikes.
But City were cut to 10 men before the break after a John Stones yellow card for a foul on Jacob Ramsey was upgraded to a red following a VAR check.
Just 11 minutes into the second half Villa also lost a man however as Matty Cash picked up a second yellow and City were able to maintain their one-goal lead until the full-time whistle.
Victory means City move 11 points clear of second-placed United with five matches left, though the Red Devils have played a game less.
And Guardiola admitted had City not managed to come from behind for their first Premier League win after conceding the first goal since December 2019, United would be “dangerous” to their title bid.
Defeat would have allowed United to trim the gap to five points, though City’s superior goal difference now essentially means two wins and a draw from their final five should be enough for yet another triumph, the club’s fifth in the Premier League era.
“Losing today would have made the last games dangerous,” admitted Guardiola, who also told BBC Sport that City are “so close” to the title after beating Villa, in his post-match press conference.
“Because United are in top form, winning a lot, and I have the feeling that if they needed to win, they are going to win.
“After our two defeats in different competitions, we knew how important it was – and for the preparation for the [Carabao Cup] final and for the Champions League game.
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“It’s close, the most difficult season of our lives we make an incredible consistency and have to finish this chapter and have to finish the few games.”
City now have a League Cup final to look forward to on Sunday against Tottenham, who sacked Jose Mourinho this week.
Ryan Mason oversaw his first game as Mourinho’s temporary successor as a Spurs side without the injured Harry Kane came from behind to beat Southampton 2-1 on Wednesday night.