Rooney also set up a chance for Jesse Lingard with a perfectly judged crossfield pass but the winger’s shot was blocked by Everton keeper Joel Robles.
But it was Martinez’s side who should have taken an early lead when Lukaku broke through with only De Gea to beat. The Belgian’s first touch, though, was clumsy and even though he managed to go wide of the United keeper, the chance had become more difficult.
When he did shoot, it was skipper Rooney who somehow got back to head off the line.
United’s neat approach play regularly created openings and Lingard’s delicate delivery set up a clear chance for Martial but from a perfectposition the ex-Monaco man blazed the ball miles over the bar.
For Everton the pace of Lukaku was always a threat but he wasted another promising situation, once again, with a poor first touch.
This one took him too wide and his resultant shot was blocked by De Gea’s right leg.