Boston’s Hunter Renfroe celebrates his three-run home run that also drove in Rafael Devers in the fourth inning Tuesday night against Minnesota. Michael Dwyer/Associated Press

BOSTON — Hunter Renfroe homered twice, the second during a five-run fifth inning that gave Boston a six-run advantage, and the Red Sox held onto the lead and their wild-card chances with a 11-9 victory over the last-place Minnesota Twins on Tuesday night.

Alex Verdugo had three hits, and Renfroe drove in five runs with his 14th career multihomer game to stake the Red Sox to a 9-3 lead. The Twins scored four in the seventh to cut the deficit to 9-8 before Kiké Hernández hit a two-run homer in the eighth to make it 11-8.

Jorge Polanco hit a two-run homer for Minnesota, and Josh Donaldson added a solo shot in the ninth off closer Matt Barnes to cut Boston’s lead to 11-9. Barnes walked Luis Arraez and Mitch Garver before getting booed back to the dugout without retiring a batter.

Ex-Twin Hansel Robles struck out Nick Gordon on a 3-2 fastball, then fanned Miguel Sanó before retiring Jake Cave on a soft liner to second for his 11th save — his first for the Red Sox.

Renfroe hit a three-run homer in the fourth inning to turn a 3-1 deficit into a one-run lead and a two-run homer in the fifth to make it 9-3.

Mitch Garver doubled and scored in the sixth before Polanco homered to chase Martín Pérez in the seventh. With runners on second and third, Hirokazu Sawamura struck Garver out and appeared to do the same with Gordon before substitute home plate umpire Phil Cuzzi called the celebrating pitcher back to the mound because the ball was tipped.

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Gordon bounced the next pitch up the middle to make it 9-8. Sanó was out on a weak grounder back to the pitcher to end the inning.

Griffin Jax (3-2) allowed nine runs on seven hits and four walks in 4 2/3 innings, spoiling a streak in which he had picked up two straight quality starts — the first two of his career.

Travis Shaw, who won Monday’s game against Texas with a walk-off grand slam in the 11th inning, hit a solo homer in the third. In the fifth, Rafael Devers doubled in one run, Verdugo hit a two-run double and Renfroe hit one onto Lansdowne Street behind the Green Monster to make it 9-3.

Red Sox starter Tanner Houck got pulled with two outs and a man on second with Boston leading 4-3 in the fifth inning. Josh Taylor (1-0) relieved him and threw one pitch to retire Arraez on a groundout.

Home plate umpire Tom Hallion took a foul ball off the top of his mask during Xander Bogaerts’ at-bat in the first inning. After a lengthy visit from the Red Sox trainer, he remained in the game. But After Bogaerts made an out, Hallion left the game.

He was replaced behind the plate by Cuzzi, who had been at second base, and the umpires worked the rest of the game as a threesome.

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