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.
Despaigne (2-0), a 27-year-old who defected from Cuba last summer, held Arizona to one run and five hits in 6 2-3 innings, walking four and striking out two.
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 Mike Bolsinger (1-4).