In a feisty opening 15 minutes to the match, both Paul Scholes and Nani were cautioned for late challenges, with no real efforts testing either keeper.
Nani then watched a long-range effort curl past the far post before Steven Pienaar forced De Gea into an outstretched save with a looping header.
Minutes later it was again Pienaar testing De Gea's ability as the South African curled a low shot towards the far corner that the Spanish stopper palmed away.
United had two opportunities before the break, with Rooney firing straight at Howard inside the area before Danny Welbeck was found by new signing Shinji Kagawa, but he could only slide wide of the post.
De Gea's palms were stung again with five minutes of the half left when Leon Osman turned and volleyed powerfully straight at the United keeper.
Everton continued to search for a goal and were yet again denied by De Gea, who dived high to his left to keep out a Leighton Baines free kick.
United's new signing Robin van Persie is expected to come on and feature in the second period.