Mike Aviles also homered and drove in two runs for Boston, which has won eight of 10 games overall after taking the final two of this three-game series.
Beckett (4-4) was booed off the mound May 10 when he allowed seven runs in 2 1-3 innings following news that he had played golf while skipping a start to rest a strained lat muscle - but he has been spectacular since.
After shutting out Seattle in a home win on May 15 by pitching seven scoreless innings and giving up four hits with nine strikeouts and two walks, Beckett allowed one run on seven hits Sunday while striking out five and walking two.
His only blemish was Juan Pierre's sacrifice fly in the eighth that gave Philadelphia its only run.
Adrian Gonzalez went 2 for 4 and now is 9 for 16 lifetime against Phillies lefty Cliff Lee.
Lee (0-2), making just his sixth start of the season after spending time on the DL with a strained oblique, had his worst start of the year. In seven innings, he allowed five runs on nine hits - both season highs. He struck out six and walked one.
The three-time All-Star and 2008 AL Cy Young winner has been pitching well this season, entering with a 1.95 ERA, but has not been getting run support some of the time or bullpen support other times.
The Phillies' offense didn't help Lee, once again, but this time the left-hander wasn't able to keep Philadelphia close.
Aviles led off with a homer for the second straight game, ripping Lee's 1-1 cutter into the seats in left.
After Aviles' RBI single in the second gave the Red Sox a 2-0 lead, Boston went ahead 5-0 in the third inning on Saltalamacchia's three-run homer that cleared the seats in center field and reached Ashburn Alley, the fan walkway behind the outfield seats.
Lee settled down after that, retiring the next 11 batters before Beckett's single off the wall in center to lead off the seventh. But the damage had been done.
Beckett was in total command against a Phillies lineup that had 15 hits the previous night. Other than the third inning, the right-hander allowed just two runners to reach second base prior to the eighth.
The Phillies threatened in the third, putting runners on second and third with one out after Lee doubled, but Jimmy Rollins grounded out to third and Pierre lined out sharply to first to keep Philadelphia scoreless.
Philadelphia scored its run in the eighth on Pierre's sacrifice fly to left that scored pinch-hitter Pete Orr, who doubled. Boston manager Bobby Valentine lifted Beckett after the right-hander walked Shane Victorino to put runners on first and second. And the bases were loaded when reliever Vicente Padilla walked Hunter Pence. But Padilla got Ty Wigginton to ground out to second to escape the jam.
The Phillies were 1 for 9 with runners in scoring position Sunday, and now are 3 for 21 in their last two games.
Notes: Phillies GM Ruben Amaro defended the club's use of a cortisone shot last Sept. 18 on Ryan Howard's injured left foot. The reaction was in response to a Philadelphia Inquirer story Sunday suggesting that the cortisone shot may have contributed to Howard's Achilles' tear last Oct. 7. ... Boston OF Cody Ross didn't play for the second straight game after fouling a ball off his left leg on Friday. ... The crowd of 45,586 was the 225th straight sellout and 241st counting postseason play. ... Philadelphia RHP Kyle Kendrick (0-3, 5.96), filling in for injured right-hander Vance Worley (elbow), is scheduled to face Washington left-hander Gio Gonzalez (5-1, 2.22) on Monday night when the Phillies host the first of a three-game series. ... Boston RHP Clay Buchholz (4-2, 7.77) opposes Orioles RHP Tommy Hunter (2-2, 4.78) when the Red Sox travel to AL East-leading Baltimore on Monday.
