City's prolific striker Erling Haaland graciously handed the ball to Gundogan to take a penalty kick in the 84th minute for what would have been a hat trick, but Leeds keeper Joel Robles had no trouble turning aside his shot.
City had run circles around Leeds with numerous excellent scoring chances before Gundogan struck in the 19th minute from the edge of the 18-yard box off a pass from Riyad Mahrez. Mahrez teed up Gundogan again eight minutes later in a carbon copy of his first goal.
Rodrigo Moreno pulled one back for Leeds in the 85th minute.
With four games left, Pep Guardiola's side have 82 points to Arsenal's 78, and if the Gunners lose to Newcastle on Sunday City will have all but locked up an illustrious third consecutive title.
Leeds, playing their first game under interim manager Sam Allardyce who was parachuted in in a last-ditch effort to avoid relegation, are teetering in 17th place - and all three teams below them have a game in hand.
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