Man City looked far more likely to get the winner after Ferran Torres had equalized for the home side, but Dallas’ breakaway goal in stoppage time handed Leeds the win.
It was the fourth league defeat of the season for Pep Guardiola’s Man City, which is 14 points clear at the top of the table ahead of a crucial Champions League game against Borussia Dortmund next week.
Leeds had only two shots throughout Saturday’s game compared to City’s 29, but it proved enough to get the win and move into the top half of the table.
“It’s a great result for us,” Dallas told BT Sport. “It was tough out there today. It’s hard enough against any team with 11 men, never mind against Man City with 10.
“It was difficult, we had to dig in and I thought we defended really, really well.”
Dallas gave Leeds the lead in the first half when his low shot from the edge of the box rolled in off the post.
But when Cooper’s challenge on Gabriel Jesus was upgraded from a yellow to a red card just before halftime following a video assistant referee review, Leeds looked set to face a long 45 minutes against the standout side in the Premier League this season.
Torres eventually got the equalizer when he found space in the box and converted Bernardo Silva’s pass, and City continued to pile pressure on the Leeds goal in the game’s final 15 minutes.
But the visiting side, which has contested a number of high-scoring games since being promoted to the Premier League, defended stubbornly.
Raphinha found himself through on goal late on, only to be tackled superbly by City goalkeeper Ederson.
Moments later, however, Dallas got the winner from another Leeds break when he slotted his shot through Ederson’s legs.
It was Pep Guardiola’s first defeat to a side managed by Marcelo Bielsa — two coaches who share a close relationship and hold each other in high regard.
City now travels to Dortmund in a bid to reach the Champions League semifinals after a 2-1 victory in the first leg.
With four trophies up for grabs this season, it needs just 11 points to wrap up the Premier League title.
Leeds, meanwhile, faces a difficult run of games with Liverpool, Manchester United and Tottenham Hotspur being three of its next four opponents.
But after beating Man City at the Etihad, Bielsa’s side will feel it can beat anyone.
Reds leave it late
Elsewhere in the Premier League, Liverpool ended a run of six consecutive Premier League defeats at Anfield with a 2-1 comeback victory against Aston Villa.
Liverpool, which suffered a humiliating 7-2 defeat against Villa last October, trailed at the break after a goal from Ollie Watkins, while Roberto Firmino’s strike on the stroke of halftime was also ruled out by a marginal offside in the buildup.
Mohamed Salah equalized when he headed in Andy Robertson’s saved shot and the game looked set to end as a draw until Trent Alexander-Arnold’s superb stoppage time strike handed the Reds a much-needed victory at Anfield.
Salah’s goal was the first Liverpool had scored at home in the league since February 7, but Jurgen Klopp’s men appear to be putting that miserable run of form behind them with a run of three consecutive Premier League victories.
The result lifts Liverpool, which will try and overturn a 3-1 deficit against Real Madrid in the Champions League quarterfinals next week, to fourth in the table, while Villa is 10th, a place below Leeds.