"The challenge for us is to look at the overall record," Posey said. "We're still in a good spot. We have to go forward."
Cody Ross hit a two-run homer for the Diamondbacks, who are 5-8 in their past 13 games. Martin Prado had three hits and drove in a run.
Nuno, acquired from the New York Yankees in a trade for Brandon McCarthy, had not allowed a run in his first 11 innings with the Diamondbacks before Posey's slam.
Bumgarner escaped a perilous sixth because of some fancy defensive plays, including his own.
Ender Inciarte and Prado each singled to start the inning. With Paul Goldschmidt batting, Bumgarner caught Inciarte taking off early for third for the first out.
Right fielder Hunter Pence, who also threw out a runner at third in the first inning, tracked down Goldschmidt's drive one step before slamming into the fence and third baseman Pablo Sandoval made a diving stop of Mark Trumbo's sharp grounder to end the inning.
Nuno breezed through the first four innings before running into trouble in the fifth. Bumgarner's one-out double started the rally. Pence was hit by a pitch and Sandoval, who had three hits, singled ahead of Posey, who homered into the left-field bleachers.
"I feel like we've been needing the big hit," Posey said. "I'm just trying to get a run on the board. Getting four across was great."
A double, an infield fielding error and a walk set up Bumgarner's slam in the sixth against Stites. Bumgarner earlier victimized Jorge De La Rosa of the Rockies.
"We had a good conversation about how we were going to attack Bumgarner," Stites said. "I just missed my spot. He's been swinging it well all year."
Goldschmidt went 0 for 4 and had his career best streak of safely reaching base end at 32 games. ... Giants 1B Brandon Belt was a late scratch due to back tightness. ... INF Marco Scutaro was a little sore according to Giants manager Bruce Bochy and was given the day off. ... Posey has three career grand slams, including the postseason. ... Arizona manager Kirk Gibson said he was going to spend part of the All-Star Break watching his son play in the Cape Cod League. ... Ross' homer gave him 501 RBIs for his career. . The Giants announced their rotation coming out of the All-Star Break, with Bumgarner opening Friday at the Miami Marlins, followed by RHP Tim Hudson, RHP Tim Lincecum, RHP Ryan Vogelsong and RHP Matt Cain.