The right-hander retired the first two batters in the sixth before allowing consecutive singles and making way for Kevin Quackenbush, who struck out pinch-hitter Roger Kieschnick to end the inning.
Despaigne got the Diamondbacks to hit into three double plays.
"A lot of deception," manager Kirk Gibson said. "We had some opportunities. He's thrown two games and he's given up one run. He's doing something right."
The Padres scored their most runs in four games. Through 81 games, they had scored one or fewer runs 27 times. They swapped places with the Diamondbacks, who had leapfrogged the Padres into fourth place after winning 3-1 Saturday night.
Huston Street pitched the ninth for his 21st save in as many chances.
The Padres scored twice in the fourth on two hits, two walks and a sacrifice fly off Bolsinger (1-4). Chase Headley drew a leadoff walk, advanced on Tommy Medica's one-out single to left and scored on Maybin's double down the right-field line. Medica scored on Alexi Amarista's sac fly.
Bolsinger allowed two runs and three hits in six innings, struck out six and walked four.
"Since I have been up here I prided myself on not walking people," Bolsinger said. "Kind of like the San Francisco game, where the one walk I gave up, the run scored. So, I just have to try to eliminate that. Besides that, everything else was pretty good."
NOTES: Nick Ahmed was selected from Triple-A Reno before the game and made his big league debut for the Diamondbacks, starting at SS and batting eighth. He grounded into a double play in his first at-bat and got his first big league hit, a single, in the seventh. ... The Padres open a three-game series against Cincinnati on Monday night, when former San Diego ace Mat Latos (1-0, 2.89) is scheduled to start against rookie Jesse Hahn (3-1, 2.38). ... The Diamondbacks are off Monday before opening a three-game series at Pittsburgh on Tuesday, when the scheduled starters are Wade Miley (3-6, 4.78) against Jeff Locker (1-1, 3.74) in a matchup of lefties.