Kemp equaled his RBI total from his previous 15 games with one big hit for the Padres, who broke open a scoreless game by batting around in the extra inning to win for just the second time in seven games.
Jedd Gyorko snapped an 0-for-13 skid with a single leading off the 10th against Joe Smith (1-2). After Yangervis Solarte and Will Venable walked, Smith struck out Justin Upton before Kemp put his drive into the corner, clearing the bases.
Derek Norris then scored Kemp with a single off Vinny Pestano.
Dale Thayer (1-0) pitched the ninth for the Padres, who had lost eight of 10.
The slumping Kemp has just one homer all year and hadn't driven in a run since May 17, but he got a big hit just down the I-5 freeway from his longtime home at Dodger Stadium.
Smith had worked 9 2/3 scoreless innings in his last eight appearances before imploding in the 10th.
Albert Pujols had two hits for the Angels, who have lost four of six to drop back to .500 (23-23). They were shut out for the third time in May.
Shoemaker yielded four hits and a walk over seven innings in his strongest start of a rocky season for the Angels, while Despaigne pitched six innings of five-hit ball without a walk.
Until the extra inning, the highlight of a pitching-dominated game was Venable's spectacular snare of Mike Trout's long drive to center in the third inning. Trout crushed Despaigne's fastball 409 feet to the deepest part of the Big A outfield, but Venable leaped at the wall and robbed him of a homer.
Shoemaker entered with just one victory in his six previous starts, but he wasn't thrown off his game when Venable's comebacker hit him in the foot in the first inning, although the right-hander did make a two-base throwing error after fielding the ball.
Angels reliever Fernando Salas allowed two runners in the eighth, but Kemp struck out looking to end it.
Padres: The tendinitis in 1B Wil Myers' left wrist has improved, manager Bud Black said. He was eligible to come off the disabled list Tuesday, but will remain inactive until he feels even better.
Padres: Hard-luck Andrew Cashner (1-7, 2.89 ERA) has lost five straight decisions despite a 3.00 ERA in that stretch.
Angels: Garrett Richards (4-2, 2.98 ERA) starts on his 27th birthday. He has never lost an interleague game.