CLEVELAND — For the second night in a row, the Twins eked out a bare minimum of offense, then watched a dramatic eighth-inning home run provide the game-winning cushion.

But there was a twist.

Instead of a Twins reliever surrendering the big blast, this time it was Cleveland right-hander Nick Sandlin who left a belt-high fastball over the middle of the plate to Willi Castro. The ball landed five rows deep in the right-field seats, and the Twins won in the offensive desert known as Progressive Field for the first time this season, 4-1 over the Guardians.

By now, the Twins know the drill when playing the Guardians, especially in Cleveland. They have met 11 times this year, and the Twins have scored a mere 32 runs in those games, more than four only once.

The solution? No choice but to make do with less.

“Everyone’s going to have to elevate their play at this point to get where we want to be. We still control everything. We still control our own destiny,” Twins manager Rocco Baldelli said. “To be at this point of the year, having struggled a little over the last month, and still be able to say ‘Hey, if we go out there and play well from here on out, we’re going to be pretty pleased with where we’re sitting at the end of the season.’ We just have to prove it.”

The Twins achieved that commendable-if-normally-elusive goal Tuesday, turning a pair of two-out RBI singles by Matt Wallner and Castro’s first homer since Aug. 25 into all the offense they needed.

OK, Byron Buxton smacked a double to the wall in right-center with two outs in the fifth inning, but sustained offensive production by Minnesota’s lineup was scarce.

As usual.

No matter how they did it, though, the victory was a critical one for the free-falling Twins, who have won only five of their last 14 games. They entered the day only 1½ games ahead of Detroit in the race for the final wild-card spot in the American League.

One day after wasting an effective two-run start by Pablo López, the Twins made a messier, but ultimately even more effective, start by rookie Zebby Matthews hold up. The right-hander had runners on base in four of the five innings he pitched in, but only once — when he centered a fastball in the strike zone for Guardians outfielder Lane Thomas in the fourth inning — did Matthews surrender a run.

Thomas drove the ball 423 feet to straightaway center, where it cleared the 19-foot wall, the ninth home run allowed in seven starts by a rookie pitcher who gave up only seven in 18 minor league games.

Rather than allow the rookie to face the Guardians for a third time on the night — Matthews has yet to pitch more than five innings in any start — Baldelli turned to his recently shaky bullpen to quiet Cleveland for the final 4 1/3 innings.

Newcomer Cole Irvin retired Andrés Giménez on three pitches in his Twins debut, and Cole Sands, Ronny Henriquez and Jhoan Duran got through the sixth, seventh and eighth innings unscathed.

Duran was given a chance to record his first two-inning save in more than two years. But when he couldn’t do it — José Ramirez led off with a double and Thomas drew a one-out walk to bring the tying run to the plate — Griffin Jax, who lost Monday’s game, was given a shot at redemption.

Consider him redeemed.

Jax struck out pinch-hitter David Fry on four pitches, the last a sweeper wide of the zone that Fry reached for. Will Brennan followed with a soft ground ball that shortstop Brooks Lee couldn’t handle, loading the bases.

But with the announced crowd of 17,391 roaring, Jax kept his cool and extinguished the drama, fooling Bo Naylor with a change-up that he dribbled up the first base line. Jax pounced on it and tagged the base, finishing off the victory.

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