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CHICAGO -- Anthony Rizzo had another series of firsts. The toughest for him to conquer was the curtain call.

Rizzo hit two home runs and drove in six to lift the Chicago Cubs to a 13-9 victory over the Pittsburgh Pirates in the third game of a four-game set.

Rizzo hit a two-run shot in a four-run fifth inning, then capped a five-run sixth with his first career grand slam to seize the lead for Chicago. The six RBIs are a career high. It was also the 23-year-old's first multihomer game.

He reappeared from the dugout briefly after his grand slam to acknowledge the crowd of 33,559.

"I didn't know what (my teammates) were saying and then I realized that's what you do," Rizzo said. "It was pretty cool."

Rizzo became the first Cubs player since Aramis Ramirez in July of 2010 to drive in six runs.

"Everything he's done up here is obviously what we've expected," Cubs manager Dale Sveum said. "We don't expect any more or any less. ... He's been spectacular since he's been here."

Pedro Alvarez hit two homers and drove in five for the Pirates, who lost for the 12th time in 15 games. Pittsburgh came into play Sunday two games behind the Los Angeles Dodgers and St. Louis Cardinals for the second wild card.

Rod Barajas went deep for Pittsburgh, and Joe Mather hit a solo shot for the Cubs.

Staked to a 6-1 lead, the Pirates were unable to hold off the feisty Cubs, who have taken five of the last six against Pittsburgh.

Rizzo's two-run, opposite field blast highlighted a four-run fifth, then he launched a 3-1 pitch into the left-center field bleachers off Jared Hughes (2-2) an inning later to put the Cubs up 10-9 and send the home crowd into a frenzy.

Rizzo recalled a game-winning homer he hit in July against St. Louis -- the grand slam didn't quite compare.

"I don't think it tops the walk-off, but it was a great game," Rizzo said. "We kept fighting the last couple of days and showing some resilience."

David DeJesus had a pinch-hit, two-run single in a three-run ninth for Chicago.

Alvarez carried the Pirates early, but they could not tack on late. The big lefty followed Gaby Sanchez's leadoff single in the fifth with an opposite-field shot onto Waveland Avenue to extend the lead to four.

After the Cubs rallied to get within one, Alvarez hit another opposite field shot in the sixth with two men on to pad the lead again. It was Alvarez's sixth multihomer game of the season. He passed Andrew McCutchen for the team lead with 29.

The Pirates had a chance to tie it with a Starling Marte leadoff triple in the seventh, but Marte was caught in a rundown on a fake to third, throw to first by Cubs reliever Jaye Chapman after Neil Walker and McCutchen failed to get the run in.

"Actually that's a forced balk, break late try to get the run to second and try to steal a run at home is what it was," Pirates manager Clint Hurdle explained. "I do believe if Starling could've shown a little more patience that play would have worked for us, but in the heat of the moment he left a little bit early."

Jeff Beliveau (1-0) allowed Alvarez's second home run, but recorded the final two outs of the sixth to earn his first career win.

Barajas homered on an 0-2 pitch with a man on and the pitcher on deck in the second inning to reach double-digits for the year.

McCutchen had an RBI single in the second and reached base four times. He has reached safely in nine of his last 11 plate appearances this series.

Pirates starter Jeff Locke was backed by a consistent flow of Pittsburgh offense, but couldn't get through the fifth inning to earn his first big league victory.

The 24-year-old Locke was staked to a 6-1 lead until things fell apart in a four-run fifth.

Mather's one-out solo homer started a string of four straight hits for the Cubs, which included Rizzo's two-run shot.

Cubs starter Chris Volstad had trouble finding the strike zone, and was hit hard when he did. The big righty gave up six runs on 10 hits through 4 2/3 innings. He walked four and struck out three.

Volstad had won three of his last four starts after enduring a brutal 24-start winless skid that spanned 13 months.

Alfonso Soriano drove in his 100th run of the season with a first-inning single to bring home Rizzo. It's Soriano's third career 100-RBI season, and first since 2005 when he had a career-high 104 with Texas.

Game notes

Pirates manager Clint Hurdle removed RHP James McDonald from the starting rotation due to a poor second half. RHP Kyle McPherson will take McDonald's turn in the rotation Wednesday against Milwaukee. McDonald is 3-5 with a 7.08 ERA since the All-Star break. ... Chicago sends LHP Travis Wood (6-11, 4.23 ERA) to the mound in the series finale Monday against Pittsburgh's RHP Kevin Correia (10-9, 4.29).