Chicago, IL (SportsNetwork.com) - Pedro Alvarez and Travis Snider homered in a five-run seventh inning and the Pittsburgh Pirates held on for a 5-4 win over the Chicago Cubs on Thursday afternoon.

The Cubs loaded the bases against Jason Grilli in the ninth inning but didn't score, giving the Pirates three straight series wins to open the season for the first time in 22 years.

Alvarez's three-run homer off James Russell (0-1) gave Pittsburgh the lead after Snider's pinch-hit two-run blast got them on the board earlier in the inning.

Right-hander Gerrit Cole (2-0) picked up his sixth straight win going back to last season after striking out 10 in six innings. He gave up four runs -- three earned -- on five hits and two walks.

The Pirates improved to 6-3 this season -- all against NL Central teams. They have taken two series against the Cubs and one against St. Louis -- only the fourth time in the last 49 seasons they have won their first three (1966, 1976 and 1992 were the others).

Starlin Castro had three hits, including an RBI single, and scored a run on a controversial play at the plate that gave the Cubs a 4-0 lead in the fourth inning.

Castro's last hit, a single in the ninth, came after Ryan Sweeney led off with a walk. Grilli struck out pinch-hitter Luis Valbuena and Welington Castillo, then walked Darwin Barney to load the bases, but Emilio Bonifacio grounded out to end the game and give Grilli his third save of the season.

"We kept battling," said Cubs manager Rick Renteria. "We fell short. ... At the end of the day we want better results."

Cubs left-hander Travis Wood was pulled after giving up a leadoff single to Neil Walker in the seventh.

Wood struck out nine, gave up three walks and four hits and was charged with a run when Snider belted Brian Schlitter's eighth pitch over the center-field wall to get Pittsburgh on the board.

Schlitter gave up a single to Starling Marte and walked Andrew McCutchen, who both scored on Alvarez's fifth homer of the season with two outs off Russell.

Earlier, Bonifacio scored all the way from first base in the third inning when he stole second and kept running after Pirates catcher Tony Sanchez threw the ball into the outfield.

A three-run fourth inning ignited by consecutive singles by Anthony Rizzo and Nate Schierholtz extended the Cubs' lead to 4-0. Castro knocked in the first run with a single, Schierholtz scored on a wild pitch and Castillo drove in Castro with a hit to left field.

Marte's two-hop throw arrived in time and Sanchez appeared to apply the tag in time to the Castro's left foot. Pirates manager Clint Hurdle came out to argue the call, which wasn't reviewed.