Rupp's early hit with Cesar Hernandez and Jimmy Rollins aboard put Philadelphia ahead to stay.
Domonic Brown and Chase Utley each drove in a late-inning run to hand the Phillies a 5-1 lead.
They would need the extra runs in the ninth when the Braves' Justin Upton bashed a three-run homer off Philadelphia's Jonathan Papelbon. The closer then proceeded to walk Freddie Freeman and Evan Gattis but finally ended the game on Chris Johnson's groundout.
Luis Garcia (1-1) notched his first major-league win as Philadelphia rebounded from losses in each of the first two contests of the season-ending four-game series.
Upton finished 4-for-5 for the National League East champion Braves.