The home side were restricted to only a handful of opportunities, Gibson with a couple of long-range shots while returning striker Wayne Rooney had one half-chance.
Wayne Rooney had United's best chance of the first half, but after the break they struggled to break down Leeds with Alex Ferguson bringing on Michael Owen, Antonio Valencia and Ryan Giggs in a desperate attempt to spark his attack.
Ferguson's side finally showed something like their best attacking play when Tevez forced an opening down the right wing, but Wayne Rooney dallied too long on his shot and the chance came and went.
Wayne Rooney, surprisingly left out of the United starting line up, also hooked a chance over, but at the other end fellow substitute Kaka rattled the home woodwork.