David de Gea was predominantly the only reason the scores remained level at the break. The Spanish stopper kept out the Toffees on a number of occasions, with Marouane Fellaini, Steven Pienaar and Leighton Baines going closest.
Everton came close to taking the lead moments after the interval when Fellaini nodded down for Leon Osman, who saw his volley clatter back off the underside of the crossbar.
Belgian midfielder Fellaini made the breakthrough by rising highest to thump home Darron Gibson's corner in the 57th minute.
The visitors looked set to equalise when debutant Shinji Kagawa set up Tom Cleverley to slot into an empty net but Phil Jagielka got back to clear off the line.
United new boy Robin van Persie made his United bow by replacing Danny Welbeck right on the midway point of the second period.
Everton sat back on their lead and invited pressure with United's two new signings Van Persie and Kagawa linking up to almost find an equaliser.
However, the pre-game favourites couldn't work a real opening in the final 20 minutes and leave Merseyside with no points.