Nicolas Pepe was sent off for the first time in his career but we stood firm to secure a point at Elland Road.
The Ivory Coast winger saw red early in the second half following an off-the-ball clash with Ezgjan Alioski.
We were forced back after that but stout defending, the woodwork and fine goalkeeping from Bernd Leno kept Leeds at bay.
And we almost snatched victory when Bukayo Saka raced through to force a save from Illan Meslier.
An attacking reshuffle saw Willian and Pepe both start, and we were collectively bright and tenacious in the early stages.
Pepe inadvertently hit the crossbar with an attempted cross from the left, and Pierre-Emerick Aubameyang slashed a shot high and wide on the turn after excellent work from Hector Bellerin.
Leeds goalkeeper Meslier wasn't tested, but Leno was. He had to save from Patrick Bamford - twice - and chances also came and went for Raphinha, Stuart Dallas and Mateus Klick as Leeds started to get on top.
Mikel Arteta brought on Reiss Nelson at half-time but our gameplan was undermined when Pepe was sent off by Anthony Taylor once the referee had checked footage of his altercation with Alioski.
Leno made a wonderful one-handed save to keep out a Dallas shot that was headed for the top corner, and substitute Rodrigo crashed a shot off the crossbar.
We looked set for a Leeds siege but, instead, we opened up the home side on the break.
One charge ended with an Aubameyang shot that was blocked by Liam Cooper's arm as the defender slid in. On this occasion, VAR was not called upon.
Saka raced through moments later but Meslier stood his ground to block the England international's shot.
Bamford headed against the post and Raphinha hit the bar as Leeds continued to threaten - but we kept a valuable clean sheet.
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