Padilla (5-7) won for the second time in three starts after a five-game losing streak. He allowed five hits, walked none and struck out five.
Rheal Cormier pitched the eighth and Jose Mesa earned his 16th save with a perfect ninth. Mesa tied Steve Bedrosian's club record with his 103rd save for the franchise. The hard-throwing right-hander also had 104 saves with the Cleveland Indians.
The Angels lost for the sixth time in their last nine games at Edison International Field despite getting 7 2/3 strong innings from starter Jarrod Washburn (6-6). But Washburn must have felt like Jean-Sebastien Giguere, who received no offensive support in the Mighty Ducks' loss to the New Jersey Devils in Monday's decisive Stanley Cup game. Washburn allowed three runs and eight hits with three strikeouts and no walks.
The Phillies got the only run it needed in the sixth inning when Jason Michaels led off with a double to left center field that Garret Anderson could not snag on a dive. After Marlon Byrd reached on an infield single, Washburn got the next two batters out, but could not get past Thome, who hit an RBI single to center.
Jimmy Rollins and Thome gave the Phillies extra runs in the eighth with solo homers. Rollins hit his third homer of the season and Thome his 15th.
Anaheim's best chance of the game came in the third inning when Scott Spiezio singled and Bengie Molina was hit by a pitch to start the frame. Benji Gil then sacrificed the runners to second and third, but Padilla got out of trouble with a strikeout and a groundout.
The Angels had another opportunity in the seventh when Brad Fullmer singled with one out, but Fullmer was thrown out trying to advance to third on Spiezio's single. Molina then singled to move Spiezio to second but Gil grounded out to end the threat.
Anaheim center fielder Darin Erstad made his first appearance after nearly two months on the disabled list and had his 10-game hitting streak snapped.