Alvarez's blast in the fourth inning put the Pirates ahead for good at 4-2 and Navarro's shot in the sixth gave Pittsburgh a 6-3 advantage.
Navarro drove in another run in the seventh while Neil Walker went 3-for-5 with an RBI single for the Bucs, who split a four-game series with the Braves.
McDonald (1-1) earned his first victory in five starts to begin the season, allowing three runs on seven hits over 7 2/3 innings. The right-hander struck out 10 batters and walked two.
Atlanta starter Mike Minor (2-2) was tagged for seven runs on eight hits over 6 1/3 frames.
Eric Hinske went 4-for-4 with an RBI single for the Braves.