Soriano also had a two-out RBI single in the first as Chicago (51-80) closed out a miserable August with a second consecutive win. The Cubs, practically locked into fifth place in the NL Central, are hoping to avoid their first 100-loss season since 1966.
"I know it's something that I don't want to be a part of," Rizzo said. "I think the magic number's down to 12 wins now. I was talking about it today. We're not going to lose 100 games. It's something we're all motivated not to do."
The Giants rallied for an 8-4 victory in Houston on Thursday night, then arrived in Chicago around 3 a.m. They mostly stayed in the visitors' clubhouse while the Cubs took batting practice, but they looked listless for much of the muggy afternoon at Wrigley Field.
"You play indoors in AC, come in at 3, 3:30 in the morning," manager Bruce Bochy said. "And it's not just the heat, it's how humid it is out there. It's a tough day. Guys were battling back. Fighting back and get the tying run up there. Just couldn't quite get it done."
It was still quite a month for San Francisco, which went 18-11 in August to increase its division lead over the Los Angeles Dodgers. It was the most victories for the Giants in a single month since they had 18 in September 2010, and they went on to win the World Series that year.
Volstad (2-9) allowed two runs and five hits in 5 2/3 innings for his second consecutive victory after a 24-start winless streak. The 6-foot-8 right-hander pitched into the seventh against Colorado on Sunday for his first win since July 10, 2011, for the Marlins against Houston.
"I felt pretty good today starting out, but the weather kinda took a little bit on me as the game kept going on," Volstad said. "I think it really did help my sinker though, as it was down and it was moving."
Madison Bumgarner (14-9) won three of his first four August starts for San Francisco, but ended up dropping his last two after another ineffective outing against Chicago.
The left-hander retired the first two batters in the third before the Cubs strung together four consecutive hits to build a 5-0 lead. Rizzo got it started with a single to center and Soriano followed with a drive to left on an 0-2 pitch for his 24th homer. Starlin Castro then singled and scored all the way from first on Welington Castillo's double to the gap in left-center.
Castillo moved to third on the throw home and headed for the plate when the ball got away from Posey.
"I didn't have it great. It didn't really stick in my pocket," Posey said. "When I went to tag, he knocked it out."
Bumgarner was late backing up home and his high return throw went off the All-Star catcher's glove, allowing Castillo to score easily.
"I was being stubborn with myself and it cost us another run," Bumgarner said. "You never want to do that."
Rizzo added his 10th homer in the fifth, a drive to left-center that skipped off the basket and caromed back onto the field. The big first baseman hustled into third, but the drive was eventually changed to a home run after a short replay review.
Carlos Marmol worked the ninth for his 17th save in 19 chances. The right-hander has converted 16 straight save opportunities.
"Bullpen did a nice job, getting some tough outs there when he had to get them," Cubs manager Dale Sveum said.
Soriano, who turned down a trade to San Francisco earlier this season, went 2 for 4 for the Cubs, who finished August with an 8-21 record. He also had a game-ending RBI single in Thursday's dramatic 12-11 victory over the Milwaukee.
"It's very hard, playing the West Coast, especially in that field," Soriano said, referring to the vetoed deal with the Giants. "It's not the team. They have a very good team, but I think it's more the city, because the weather."
Posey will start at first base on Saturday. Bochy said before the game he would get a day off this weekend. ... The Cubs recalled reliever Jeff Beliveau from Triple-A Iowa and sent fellow LHP Brooks Raley to the minors. They also announced they will recall OFs Tony Campana and Dave Sappelt and INF Adrian Cardenas when major league rosters expand on Saturday. Raley's season is over, and LHP Chris Rusin will be recalled on Tuesday to start at Washington. RHP Miguel Socolovich, who was claimed off waivers from Baltimore on Aug. 23, will be added to the active roster on Sunday. Backup C Anthony Recker, who was acquired in a trade with Oakland, is expected to join the team on Tuesday. ... RHP Tim Lincecum (7-14, 5.30 ERA) starts for San Francisco on Saturday against RHP Justin Germano (2-4, 5.91 ERA). Lincecum is 2-0 with a 1.59 ERA in four career starts at Wrigley Field.