Bielsa's first win in five meetings against Pep Guardiola propels Leeds up to ninth in their first season back in the English top flight for 16 years.
City offered the second-placed Red Devils little extra encouragement that there was a route back into the title race as Riyad Mahrez and Kevin De Bruyne both struck twice.
Premier League: Manchester City stretch unbeaten run to 28 games with win over Wolves, open up 15-point gap at top
The victory was Manchester City's 21st in a row and their 15th straight Premier League win.
Premier League: Manchester City open up 10-point lead after beating Everton; Burnley fightback to hold Fulham
With the victory, Manchester City extended their English top-flight record winning run to 17 games.
West Ham defeated Crystal Palace to occupy the fourth Champions League place.
For the first time ever, Guardiola saw one of his teams concede five goals in his 686th game as a manager with City, Bayern Munich and Barcelona.
Premier League: Midfielder Ilkay Gundogan becomes latest Manchester City player to test positive for COVID-19
Gundogan is the third City player to return a positive test this month, following Aymeric Laporte and Riyad Mahrez.
All players or club staff who have tested positive will self-isolate for a period of 10 days.
A video posted on social media in Iceland showed Foden and Greenwood meeting women from outside the team bubble. Reports said they had brought them back to England's team hotel, but the manager said that was not the case.
Manchester City said both Riyad Mahrez and Aymeric Laporte have not displayed any symptoms and are in self-isolation.
FA Cup: Manchester City edge out Sheffield Wednesday to seal quarter-final berth; Norwich beat Tottenham on penalties
Sergio Aguero’s second-half goal proved enough for holders Manchester City to beat second-tier Sheffield Wednesday 1-0 on Wednesday and reach the FA Cup quarter-finals, but Pep Guardiola’s side made hard work of it.
Aguero scored three goals, and had an assist for Riyad Mahrez, who scored two in a game for the first time in 16 months
League Cup: Manchester City boss Pep Guardiola explained strategy for United match in just 15 minutes, says Kevin De Bruyne
Guardiola opted to play without a recognised striker at Old Trafford, giving De Bruyne and fellow midfielder Bernardo Silva licence to push forward centrally and the move worked perfectly as City scored three times before halftime
Liverpool star Sadio Mane beats out Mohamed Salah, Riyad Mahrez to be named African Footballer of the Year for 2019
Mane finished ahead of Riyad Mahrez and Salah in a poll of national team coaches and captains, and was handed his award at the Confederation of African Football’s annual gala in Hurgada, Egypt
League Cup: First-half goalfest sees Manchester City cruise to semi-final first-leg win over rivals United
In the end, Manchester City came away from Old Trafford on Tuesday with a 3-1 victory but with a hint of frustration that the score wasn't even bigger after a one-sided first leg of the English League Cup semi-finals
Premier League: Leicester win could be the perfect trampoline for Manchester City to string together a sequence of results to close gap on Liverpool
At the final whistle, Pep Guardiola’s Man City having gained three points are on 38 points, while Brendan Rodgers’ Leicester remain on 39, 10 points off Liverpool
Premier League: Manchester City beat Leicester 3-1, show stomach for taking title fight to Liverpool
If any team has a chance of stopping Liverpool marching to a first English league title in 30 years, it looks to be Manchester City rather than Leicester.
Premier League: Manchester City back to winning ways after beating Burnley; Crystal Palace edge past Bournemouth
City bounced back from their disappointing draw at Newcastle by beating Burnley 4-1 in the Premier League on Tuesday, displaying the kind of fluent attacking play that has often eluded Pep Guardiola’s team lately.
Premier League: Manchester City weathered Chelsea's early onslaught before gradually working up field in 2-1 win
The match ended 2-1 in favour of the Manchester City with goals from Kevin De Bruyne and Riyad Mahrez, nullifying the strike from Chelsea’s N'golo Kante. The win helps City switch places with Chelsea on the points table.
Manchester City returned to winning ways with a 2-1 success over Chelsea at the Etihad Stadium on Saturday, ending the Londoners’ run of six straight victories