Norwich caused a few problems with some early set-pieces and Ozil should have opened the scoring for Arsenal when he was picked out in the box by Nacho Monreal. The German dragged his effort off target, with Sebastian Bassong clearing the danger.
Sanchez drew the first good save out of John Ruddy, forcing the England goalkeeper to parry a fierce shot from inside the box after a fine run from Santi Cazorla.
But Ruddy proved his side’s undoing with a poor clearance in the 28th minute, allowing Sanchez to slip the ball through to Ozil, who clipped a fine finish into the far corner from the left side of the area.
Alex Neil’s team had been comfortably second best but they snatched an equaliser just before the break. Robbie Brady fed the ball into the feet of Grabban, who turned Gabriel superbly before rolling the ball beneath Cech.
And Hoolahan wasted a glorious chance for a second in stoppage time as he side-footed over the crossbar when picked out unmarked at the far post by Andre Wisdom.