Granderson hit an 0-and-1 pitch into the right-field seats against Papelbon (0-1) for his second homer in three games with his new team.
Then, after three walks, Mark Teixeira drove in the final run on a groundout as the Red Sox wasted an outstanding performance by John Lackey in his first appearance since signing an $82.5 million, five-year contract as a free agent in December.
Chan Ho Park (1-0) allowed one hit in three scoreless innings after Andy Petitte's start, and Mariano Rivera pitched the 10th for his second save.
The Yankees set a record for the modern era with their 17th straight win in regular-season games that were tied after seven innings. They equaled the 1906 New York Giants at 16 on Tuesday night when they beat the Red Sox 6-4 with single runs in the eighth and ninth.
Lackey allowed three hits in six innings and left with a 1-0 lead.
David Ortiz had gone 0-for-7 in his first two games following the worst of his first seven seasons with Boston. And after Tuesday night's game, he responded with an expletive-filled tirade when asked about his slow start.
On Wednesday, though, with the crowd chanting "Papi! Papi! Papi!" he gave the Red Sox a 1-0 lead in the third with his first hit in nine at bats. His two-out single scored Dustin Pedroia, who led off with a double. But in his other three at-bats, Ortiz ended innings with two strikeouts and a groundout.
The Yankees tied the game in the seventh after Scott Schoeneweis replaced Lackey. Jorge Posada doubled with one out but Granderson, obtained in a trade with Detroit, struck out. Daniel Bard relieved and, on an 0-and-2 count, allowed Nick Swisher's tying single.
Kevin Youkilis was beaned in the fifth by Pettitte and went to first base without incident. That moved Victor Martinez, who had singled, to second with two outs. Then Ortiz struck out on a low pitch outside the strike zone.
Derek Jeter led off the sixth and was hit by Lackey on a 2-2 pitch, prompting home plate umpire Paul Schrieber to issue warnings to both dugouts. Nick Johnson flied out before Teixeira walked, putting runners at first and second. Alex Rodriguez then hit a hard grounder to the left of third baseman Adrian Beltre, who scooped it up cleanly and started an inning-ending double play.
The Yankees had runners in scoring position in two innings against Lackey.
Teixeira walked with two outs in the first, but Rodriguez flied out. After a perfect second, Lackey gave up a two-out single to Jeter in the third before striking out Johnson.
Robinson Cano singled with two outs in the fourth but was caught stealing. In the fifth, Granderson hit a one-out single to center field and stole second, but Lackey retired Swisher on a fly ball and Brett Gardner on a grounder.
Cano has hit safely in 16 consecutive games against Boston. … Teixeira went 0-for-12 with three walks in the series. … Lackey began the last two seasons on the Los Angeles Angels disabled list. … Manager Don Zimmer, outfielders Jimmy Piersall and Tommy Harper and infielder John Valentin were named to the Red Sox Hall of Fame by a 14-member panel of team executives, media members, booster club representatives and historians. Eddie Kasko was picked as a non-uniformed member. He was a vice president, manager, coach and player for the Red Sox.