Beckett (4-4) tamed the Phillies on one run, yielding seven hits and a pair of walks while striking out five in the performance -- his second win in two starts.
The Red Sox ace tossed 72 of his 103 pitches for strikes, staking Boston to a victory in the rubber match of their three-game series at Citizens Bank Park.
Mike Aviles socked a solo homer in the first and added an RBI single in the next frame to put Boston up 2-0, and Saltalamacchia followed with his three-run shot in the third to break the contest open.
The Phillies' Cliff Lee (0-2) ran his winless streak to six starts, the longest such stretch to start a season in the left-hander's career.
He was touched for five runs on nine hits over seven frames, walking one and fanning six.