Rodriguez hit a two-run shot in the fourth and added a three-run blast, his 30th of the season, into the upper deck in right field in the seventh. It was the 11th multi-homer game of his career and third this season.
"It's been a good season for me, a great year for the Cubs and a great year for Sammy," Rodriguez said. "When you hit 30 homers, you reach another level."
The Cubs obtained Rodriguez, who hit 36 homers in 1996 for the Expos, in a trade from Montreal last December to give them another home-run threat.
"In the past, once we got past Sammy in the lineup we were pretty much relying on three singles to score a run," Cubs manager Jim Riggleman said. "We have been very reliant on the home run. We wouldn't be where we're at without the long ball this year."
Sosa went 1-for-3 with a single, two walks and a run scord. He has 46 homers, one behind Mark McGwire for the major-league lead.
Servais hit a two-run homer, his sixth, and Blauser added a solo shot, his third, as the Cubs scored five runs on three homers in the fourth off Kirk Rueter (12-8).
"It seems like every time we make a mistake, they hit it out," Rueter said. "I could tell (my pitches) were up by the way the Cubs were swinging."
Chicago added five more in the seventh on Rodriguez's second homer, an RBI single by Lance Johnson and an error.
"You go through stretches when you hit homers, and you go through stretches when you give them up," Giants manager Dusty Baker said. "I don't ever remember a stretch this bad."
The Giants have allowed 24 homers in their last seven games.
"It's hard to win when you can't keep the ball in the ballpark," Baker added. "I don't think they could hit more home runs if you told them what was coming. I don't think they could hit any more if it was batting practice."
Steve Trachsel (12-6), who has won six of his last seven decisions, allowed two runs on seven hits in seven innings. He has allowed two earned runs or fewer in 12 of his 24 starts this season.
With the win, the Cubs temporarily moved into a tie with the New York Mets in the race for the NL wild-card spot. The Mets were to play Wednesday night at St. Louis.
The Giants, who have lost seven of nine, fell three games behind the Cubs.
Charlie Hayes and Rich Aurilia hit solo homers for the Giants. It was Hayes' ninth of the season and the eighth for Aurilia.
Sosa walked in the second and fourth innings, grounded out in the fifth, singled in the seventh and struck out in the eighth.
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