Bryson Stott launched a two-run home run among his two hits, Kyle Schwarber hit a solo homer, and Trea Turner added a solo home run and two-run triple for the Phillies, who have won five in a row.
Phillies starter Michael Lorenzen (8-8) tossed six innings and allowed eight hits and four runs, three earned, with five strikeouts and two walks.
Luis Rengifo hit two solo homers and singled and Randal Grichuk had three hits, including a solo home run and two doubles. Shohei Ohtani also had three hits and two RBI, and Nolan Schanuel chipped in two hits.
Angels starter Tyler Anderson (5-6) gave up seven hits and six runs with three strikeouts and three walks in five-plus innings.
Turner's home run in the eighth inning gave Philadelphia a commanding 12-5 lead.
Los Angeles scored twice in the ninth, highlighted by Ohtani's RBI double.
The Angels went ahead 1-0 when Rengifo hit a solo homer to right in the second. The Phillies quickly tied the game in the bottom of the inning when Harper launched a solo shot to right, his 14th of the season and ninth in August.
Los Angeles regained a 2-1 lead in the third when Ohtani's infield single and Lorenzen's throwing error allowed Grichuk to score.
The Phillies equalized at 2 in the bottom of the third when Schwarber crushed a solo homer off the facing of the second deck in right for his 37th of the season.
Rengifo's second solo homer, this time in the fourth, put the Angels ahead 3-2. It's the fourth career multi-homer game for Rengifo.
Ohtani hit an RBI single in the fifth for a 4-2 advantage.
Philadelphia took a 6-4 lead in the sixth when Bohm ripped his three-run homer to left and Johan Rojas added a sacrifice bunt and an RBI. Turner extended his hitting streak to 10 in a row with a two-run triple down the left field line for an 8-4 advantage.
Grichuk lofted a solo homer to left in the seventh and the Angels closed within 8-5.
In the bottom of the seventh, J.T. Realmuto (two hits) contributed an RBI single to right, and Stott added a two-run homer for an 11-5 lead.
—Field Level Media