Overbay and Chris Young hit back-to-back homers an inning earlier to send the game into extras.
David Hernandez (4-3) stranded two runners in the top of the 10th to earn the win for the Diamondbacks, who lead the NL West by 9 1/2 games. The second- place Giants lost 3-0 to the Dodgers on Saturday.
"It just seems like it's a different person every night," said Overbay. "We got down early. They shut us down, we got to the ninth and were able to tie it up. We got to the 10th, great at bats, and we were able to put one across."
Joe Thatcher issued the decisive walk in the home 10th after Brad Brach (0-1) allowed the Diamondbacks to load the bases.
James Darnell hit his first major league home run for the Padres, who have lost 14 of their last 16 games.
Darnell's two-run blast broke a 2-2 tie in the sixth and chased Diamondbacks starter Wade Miley. Later in the frame, Padres starter Tim Stauffer bunted home Luis Martinez from third to make it a 5-2 game.
Heath Bell took the hill in the bottom of the ninth and Young greeted him with a homer to left. Overbay then belted a 2-1 fastball to left. The ball barely cleared the fence, resulting in a 5-5 tie.
"That doesn't make me feel good, especially the way we've been losing games," said Bell . "I go out there and blow it, hang a pitch and Overbay gets a good piece of wood on the pitch."
Hernandez allowed runners to reach first and second with two down in the top of the 10th, but popped out pinch-hitter Will Venable to escape.
Brach walked Upton, allowed a Montero single and intentionally walked Blum to load the bases in the home 10th. He fanned Young for the second out of the inning before exiting in favor of Thatcher, who walked Overbay on four pitches to push across the deciding run.
Darnell's RBI groundout and Alberto Gonzalez's sac fly gave the Padres a 2-0 lead in the second.
The Diamondbacks, winners of 15 straight home games and 16 of their last 18 overall, responded a half-inning later with consecutive RBI doubles from Young and Overbay.
The Diamondbacks' 15 straight home wins is a franchise record and marks the longest such streak in the major leagues this season...Miley allowed five runs on eight hits over five-plus innings, while Stauffer surrendered three runs on six hits over 5 1/3 innings...Montero has hit safely in a career-high 18 straight games...Following the game, the Padres filed a protest with major league baseball, claiming that Montero did not touch third base on the final play. However, according to rule 4.09(b), only the batter and the runner advancing from third base must touch their respective bases on a game-ending walk.