Wilson (10-6) notched his sixth victory in seven starts, stymieing the Athletics on three hits and two walks. The left-hander struck out eight, placing 80-of-119 pitches for strikes.
Ernesto Frieri recorded the game's final two outs for his 24th save as the Angels snatched their second straight win over Oakland.
The loss was hung on Oakland's Dan Straily (6-3), who yielded two runs on eight hits over seven innings.
The American League West-leading A's retained a two-game lead over Texas despite the loss after the Rangers fell Saturday to Baltimore.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
Theater accidentally screens 'Nymphomaniac' trailer instead of Disney's 'Frozen'