Leeds remarkably run out 2-1 winners at the Etihad Stadium to make it three consecutive Premier League wins for the first time in 18 years.
Dallas’ first-half goal had given the visitors the lead.
The Northern Ireland international opened the scoring after 42 minutes and then grabbed the winner against the run of the play with a cool finish between Ederson’s legs in injury-time.
In between, Leeds had seen their skipper Liam Cooper dismissed after launching his studs on Jesus on the stroke of half-time though he won the ball, caught the Brazilian above the knee with a raised boot.
Referee Andre Marriner signalled a yellow but after being advised to check on his screen by VAR, it turned into red.
As Cooper strolled off, the unlucky was sacrificed so Bielsa could bring on Pascal Struijk to reinforce the defence.
Ferran Torres level for the dominant home side after 76 minutes in the second half with a right-footed equaliser.
With the hosts pressing on for a winner, Dallas grabbed a second goal in the 91st minute.
City’s pressing left them vulnerable at the back. Meslier’s throw-out saw Leeds move up the field with Alioski playing a one-two with Raphinha and then sliding in Dallas.
He finished like a natural centre-forward to cap a crazy day at The Etihad to secure a memorable three points for Bielsa’s men on the road.
It was only the second time in 29 matches City had failed to win, and that despite registering 30 shots on goal.
But the shock result does give Manchester United the faintest glimmer of hope to Manchester United in the title race and City may only be eight points ahead when they next play in the league at Aston Villa on April 21.
Pep Guardiola will be disappointed there weren’t more players who put their hand up for selection.
Kevin De Bruyne was among those rested on the bench with Germany in mind.
Leeds manager Marcelo Bielsa, an inspiration for Pep Guardiola, drafted in winger Helder Costa to replace Jack Harrison who is loan from City at Elland Road.
The Whites climb up to ninth in the league and they next host Liverpool at Elland Road.
Guardiola’s side are in Champions League action against Borussia Dortmund in midweek before an FA Cup semi-final clash with Chelsea.
The hosts, who sit top of the league, then travel to Aston Villa for their next Premier League game.