Philadelphia sent 10 men to the plate in the second inning on its way to snapping a six-game losing streak.
Fontenot hit a two-run homer to kick off the frame and Shane Victorino doubled in two runs later in the inning as part of a five-RBI performance.
Victorino had an RBI single in the first and hit a two-run homer in the fourth.
Fontenot had gone hitless in his first 20 at-bats in June before producing three singles Thursday against the Los Angeles Dodgers.
J.J. Hardy's two-run homer brought Baltimore within three in the seventh inning, but Antonio Bastardo struck out the side in the eighth and Jonathan Papelbon worked the ninth for his 16th save.
Joe Blanton (5-6) gave up five runs on seven hits with seven strikeouts over 6 2/3 innings to get the win.
Jake Arrieta (2-8) was pounded for nine runs on 11 hits in four frames.