Anthony Rizzo thrived in the leadoff spot again, extending his career-high hitting streak to 13 games by going 2 for 3 with an RBI as Chicago won its second straight to improve to 35-34.
Jose Pirela and Yangervis Solarte each had a solo homer for the Padres, although Pirela's error allowed the winning run to score.
Hector Rondon (2-1) pitched a scoreless inning for the win. Davis had runners on second and third with one out, but struck out Wil Myers and got Hunter Renfroe to ground out for his 14th save in 14 chances.
Kirby Yates (1-1) allowed one unearned run to get the loss.