After Pages delivered yet another clutch hit off Wandy Peralta (3-1), Edman brought him home with a fortunate bouncer that ricocheted off second base.
Jackson Merrill slugged a one-out RBI double in the 10th for San Diego, but Tanner Scott finished for his 12th save.
Kirby Yates (4-2) struck out two in a hitless ninth.
Tyler Wade had a three-run triple for the Padres, who have lost four of six.
Nick Pivetta yielded five runs and eight hits over just four innings in his second straight rough start for the Padres, while Dustin May gave up six hits and four walks over five innings for LA.
Shohei Ohtani led off with a 111-mph double and scored on a double by Freddie Freeman, who had three hits. Manny Machado had an RBI double for San Diego in the first.
Smith put the Dodgers up 5-3 in the third with a two-run homer, his sixth. Wade cleared the bases for the Padres later in the third with a two-out drive that Teoscar Hernández couldn't catch while sliding in right field.
Key moment
Hyeseong Kim had a tying double in the fifth for the Dodgers, and neither team scored again until Pages drove in Max Muncy.
Key stat
In front of Petco Park’s usual lively bipartisan crowd for this rivalry, both starting pitchers were battered by these powerhouse lineups for 11 combined runs in the first three innings.
Up next
Dylan Cease (1-5, 4.72 ERA) pitches Tuesday for San Diego. The Dodgers hadn't announced the next patch on their injury-riddled rotation.
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AP MLB: https://apnews.com/MLB
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