Pep Guardiola’s side were seconds away from a damaging draw at the Etihad Stadium after Bernardo Silva’s early opener was cancelled out by Marcus Rashford’s penalty.
But Nunes’s last-gasp strike sparked wild celebrations from Guardiola and his players as they climbed to third place in the Premier League.
With the race for a top-five finish approaching a tense climax, Portugal midfielder Nunes, converted to right-back lately, could not have picked a better time to net his first league goal for City.
City’s 15th successive home league win against Villa wasn’t quite as stunning as the fightback from two goals down that brought them the Premier League title on the last day of the 2021-22 season.
But it could prove almost as lucrative, with a place in the Champions League now within their control.
With four games left, City will remain at least fifth even if fourth-placed Nottingham Forest, fifth-placed Newcastle and sixth-placed Chelsea each win their game in hand.
After winning the Premier League six times in the previous seven seasons, City have been reduced to fighting for a place in the Champions League at a time of year when they are usually in the title hunt.
City’s decline has already been remarkable enough, but enduring a first season without Champions League action since 2010-11 would be a new low and this was a vital step in avoiding that fate.
City will turn their attention to the FA Cup semi-final against Nottingham Forest at Wembley on Sunday, while Villa must bounce back from a painful loss in time for their own last-four clash with Crystal Palace on Saturday.
Villa were eliminated from the Champions League quarter-finals last week after narrowly failing in their bid for a dramatic fightback against Paris Saint-Germain in the second leg.
This was another blow for Unai Emery’s seventh-placed side, who are two points adrift of the top five with four games left.
With Rashford on loan from Manchester United, it was no surprise that his name was loudly jeered by City fans before kick-off.
The England forward almost silenced the boos just 19 seconds after kick-off when he slalomed past Ruben Dias for a low drive that smacked off the far post.
After that narrow escape, Silva landed the first blow for City in the seventh minute.
Omar Marmoush was the catalyst with an incisive surge into the Villa area before cutting his pass back to Silva, whose stinging strike from 10 yards was too powerful for Emiliano Martinez’s awkward attempted save to keep out.
Silva’s first goal since December provoked an immediate response from Villa.
In the 18th minute, Jacob Ramsey induced a lumbering challenge from Dias, who tripped the midfielder for a penalty that was only awarded by referee Craig Pawson after VAR told him to consult the pitchside monitor.
Guardiola was furious with the decision, earning a booking for his tirade at the fourth official.
Rashford kept his nerve, sending Stefan Ortega the wrong way from the spot for his fourth goal since his loan move in the January transfer window.
Rashford’s blistering speed was a constant danger to City and he easily out-paced their back four for a shot that Ortega blocked with his legs.
However, City got to grips with Rashford better in the second half as they pushed for a winner.
Nunes was their saviour in the fourth of five minutes of stoppage time when he met Jeremy Doku’s low cross with a superb finish from the most acute of angles six yards from goal.
Guardiola’s frenzied fist-pumping dance of joy underlined the significance of a crucial result in a turbulent season that could still have an uplifting finale. (AFP)
