The German midfielder swept home two low drives from the edge of the box - both assisted by Riyad Mahrez - to put the Blues firmly in control.
But a late missed penalty by the City skipper and a Leeds goal shortly after set up an edgy finish to the game that City eventually saw out.
It is City’s 10th successive Premier League win and it moves the Blues four points clear of Arsenal at the top of the table.
WHAT HAPPENED?
City assumed control almost from the word go with Sam Allardyce’s Leeds defending in numbers and attempting to cut off the supply lines.
That, however, is easier said than done with this Manchester City team and camping in and around your own box at the Etihad can result in a very long 90 minutes.
The visitors held firm for the first 15 minutes or so, but after that, the chances started to come with the frequency of buses leaving Piccadilly Gardens on a Monday morning.
The first fell to Erling Haaland on 17 minutes who saw his low shot saved by Joel Robles, but City took the lead in the next attack when Mahrez cut inside from the right before finding Gundogan on the edge of the box and City skipper swept a low shot into the bottom right-hand corner to make it 1-0.
Haaland had another good chance on 24 minutes after an outrageously clever flick by Kevin De Bruyne, but he skewed an angled drive past the post.
However, if anyone has credit in the bank in front of goal, it is most definitely Haaland.
Just before the half-hour, the Blues increased the lead with a goal that had more than a touch of déjà vu about it as Mahrez again cut in from the right, spotted Gundogan free on the edge of the box and his short pass was again swept home by the Germany international - this time into the opposite corner of the Leeds net.
Ederson was tested shortly after, saving a point-blank header from a corner with what would be Leeds’ only shot on target in the first 45.
Pep Guardiola’s perfect scenario would have been to have a healthy lead at the break and then rest two of three of his stars ahead of the Real Madrid clash, but the 2-0 lead was the least a dominant City deserved.
There was a sizeable blow for the Blues eight minutes into the second period when Nathan Ake sat on the turf and immediately indicated his afternoon was over with what is at present an unspecified injury.
The Leeds-born Haaland’s day of frustration against the team his dad once represented continued with a spin and shot that struck the outside of post on 62 minutes suggesting it might not be his day.
City probed continuously without ever having to overly exert too much energy, with Leeds seemingly happy to limit the margin of defeat and the Blues content to see out the game and claim three more crucial points.
But on 83 minutes, a terrific dart into the box by Phil Foden resulted in a foul and a penalty was awarded by referee Andrew Madley.
Haaland handed the ball to Gundogan, but his shot struck the post thanks to a fingertip save by Robles and Leeds survived - and within 60 seconds, the visitors were back in the game as sub Rodrigo drilled a low shot past Ederson from 18 yards to set up a nervy finish.
Ultimately, the Blues held out and the result is all that matters at this stage of the season.
WATCH: Gundogan applauds ‘important win’
Classy Gundogan
As he approaches his 300th appearance for City, it games like this that underline how important he is to this team - and has been for so long.
Gundogan purrs around the pitch, effortlessly controlling the game with his intelligent passing and movement.
Of course, he always has a goal or two in him and even from a deeper role against Leeds, his two goals were down to timing and accuracy.
His spot-kick miss meant he couldn’t complete his first City hat-trick on this occasion, but was otherwise flawless.
Such a class act.
De Bruyne irreplaceable
He may not have scored or assisted a goal against Leeds, but when Kevin De Bruyne plays City are a different animal.
It goes without saying the Blues are excellent even if KDB doesn’t start, but he is such a clever footballer with incredible vision - one of the best players in world football.
Few can do what he does on a regular basis, and it is a privilege to watch him play.
He was a constant threat throughout against Leeds and played the full 90 minutes and is key to our efforts to add more silverware to the trophy cabinet in the weeks that remain.
In short, he’s irreplaceable.
STAR MAN: GUNDOGAN
Two goals and a masterful display by our captain.
Honourable mentions for De Bruyne, Rico Lewis and Aymeric Laporte who all had fine games as well.
WHAT IT MEANS...
City increase the lead over Arsenal to four points with both teams now having played 34 games.
The Gunners can reduce that deficit back to one point if they win against Newcastle United at St James’ Park on Sunday afternoon.
WHAT’S NEXT?
City jet out to Spain to take on Real Madrid in the Champions League semi-final, first leg on Tuesday, kick-off 20:00 (UK).
Then the Blues travel to Goodison Park to take on Everton on Sunday May (14:00 kick-off) where another testing 90 minutes await with the Toffees desperate for points to avoid the drop.
PEP REACTION
“We played an exceptional game. Our possession game was really good. First half was exceptional.
“We were maybe not as clinical as we should be. The second half, we cannot forget it is three games in six days with a lot of mental pressure.
“After Arsenal we were drained a bit and we kept going against Fulham and West Ham - tough opponents. At the end, the game could be over with the penalty. But they score and we have to suffer. But we played really, really good.
“I would say it was a comfortable game for him [Ilkay Gundogan] because he was not pressed much. But Gundo... what can I say?
“He can do everything. As a holding or attacking midfielder, he is so intelligent. We are delighted to have him.”
TEAM NOTES
City: Ederson, Lewis, Ake (Walker 55), Laporte, Akanji, Gundogan (Rodrigo 90+3)), De Bruyne, Foden, Alvarez (Bernardo 87), Mahrez, Haaland
Subs: Ortega Moreno, Dias, Phillips, Stones, Grealish, Gomez
Leeds United: Robles, Kristensen, Wober, Firpo, Ayling, McKennie, Forshaw (Struijk 80), Roca (Greenwood 58), Harrison (Summerville 65), Bamford (Aaronson 80), Gnonto (Rodrigo 58)
Subs: Meslier, Koch, Rutter Gray
STATS AND MILESTONES
City have won the last four Premier League games against Leeds by an aggregate score of 16-2.
Bernardo made his 300th appearance for the Blues and Rodrigo his 200th as both came on as late subs.
City have lost just two of their last 61 Premier League games in the Saturday 3pm kick-off slot (W51 D8), with both of those losses coming at home to Crystal Palace (December 2018 and October 2021).
This was City’s 10th Premier League win on the bounce.
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