Raheem Sterling gave City a first-half lead, but the home side was much-improved after the break and levelled on the hour-mark.
Both sides went for broke in the last half-hour but it ended honours even.
City started as though they had a point to prove after last weekend’s demoralising loss to Leicester.
Perhaps sensing Leeds would come out of the blocks flying, City began by keeping the ball almost exclusively for the first 20 minutes.
Crisp passing and movement, the hosts looked bewildered as they chased shadows, unable to live with the fluidity and pressing.
With only three minutes played, City were a coat of paint form going ahead as Kevin De Bruyne spotted 20-year-old keeper Illan Meslier anticipating a cross into the box from the left and instead struck the free-kick towards the near post, but the ball struck the woodwork.
It was an audacious effort that deserved better, but Leeds survived.
The next notable effort came when Sterling weaved to the corner of the six-yard box but though his inviting found Ferran Torres, his low drive was cleared off the line by a defender.
The respite didn’t last long, however, with City taking the lead two minutes later as Torres fed Sterling on the left of the box and the England forward jinked inside two challenges before burying a low drive into the bottom corner of the net.
Leeds were clinging on at times, but they weathered the worst of the storm and gradually began to threaten the City rear-guard.
On 37 minutes, Leeds almost equalised when a smart passing move saw the overlapping Stuart Dallas denied by a good Ederson save.
Then a mistake by Benjamin Mendy allowed Luke Ayling a diagonal run on goal and after selling a clever dummy, he too was denied by a smart Ederson stop.
Marcelo Bielsa’s renowned tactical nous was evident after the restart with a few telling tweaks to their formation quickly paying dividends.
Eventually, the much-improved hosts levelled just pas the hour as a corner came in and mistimed his punch and the ball hit Mendy and fell to Rodrigo – Leeds’ Rodrigo – who tapped into the empty net from a yard or so out.
The Brazilian keeper more than made up for his mistake on 70 minutes with a stunning fingertip save onto the crossbar from Liam Cooper’s powerful header.
City regained control for the last 20 minutes or so and had three half-appeals for penalties in the time that remained, two of which were looked at by VAR, but nothing was given.
Ultimately, the points were shared against a Leeds side who are likely cause problems for many Premier League sides this season.
The Portuguese looked comfortable in possession and played good, incisive passes out from the back.
There was an air of calmness about the 23 year-old who clearly won't be ruffled easily.
In the second-half, he and his team-mates were regularly put under pressure but he did well, putting in solid, well-timed challenges when needed.
All in all. a solid debut by our new centre-back.
What it means
City move on to four points from three games and move to tenth place in the table with a game in hand over most clubs above.
City have a two-week break before the next fixture - a Premier League home fixture against Arsenal on October 17 (5.30pm kick-off).
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