Utley hit a home run for the second straight night and Shane Victorino added a solo shot as part of a three-RBI game.
Philadelphia jumped over the New York Mets into a half-game lead in the National League East. Florida is just 1 1/2 games behind the Phillies.
It was Philadelphia's fourth straight win and Washington's eighth straight loss.
The big fifth inning gave the Phillies a 7-3 lead, enough of a cushion for 46-year-old Jamie Moyer to pick up the 240th win of his career. Moyer (10-6) gave up three runs on six hits over six innings and tied Frank Tanana for 12th place in victories all-time among left-handers.
Brad Lidge, pitching in his fifth straight game, earned his 26th save.
Tim Redding (7-6) gave up seven runs on 10 hits in four-plus innings to take the loss, his third straight.