NEW YORK -- While the rest of his New York Yankees teammates were doing enough to win close postseason games, Aaron Judge was often ending his postseason at-bats without productive results.

At least until Tuesday.

Judge hit his first homer of the postseason, a two-run shot in the seventh inning that padded the lead as the Yankees earned a 6-3 victory over the Cleveland Guardians in Game 2 of the American League Championship Series.

The Yankees hold a 2-0 lead in the best-of-seven series as it shifts to Cleveland beginning on Thursday.

New York manager Aaron Boone said of Judge's blast, "It gave us some breathing room there."

Judge hadn't gone deep in the postseason since Game 5 of the 2022 AL Division Series against Cleveland. On Tuesday, he sent a 1-1 fastball from Hunter Gaddis onto the netting in Monument Park beyond the center field fence to give the Yankees a 6-2 lead.

"I was excited it went out," Judge said. "You never know on these windy, chilly nights what that ball is going to do when you hit it to center here, but the ghosts were pulling out there to Monument Park, that's for sure."

It was just his third hit of the postseason but his 14th career playoff homer.

"It's a big swing for Judgey," New York first baseman Anthony Rizzo said. "He's had really good at-bats and come up in big situations. To get the home run, it was a really easy swing, and he's the best in the business at that."

In the first inning, Gleyber Torres scored New York's first run when Cleveland shortstop Brayan Rocchio dropped Judge's popup. Judge also lifted a sacrifice fly in the second to make it 3-0 after the Guardians opted to intentionally walk Juan Soto to load the bases.

Alex Verdugo added an RBI double in between Judge's first two plate appearances. Another run scored in the sixth when Rizzo doubled to right and a bobble by Will Brennan allowed Anthony Volpe to race all the way home from first.

The New York offense proved sufficient on a rocky night for Yankees ace Gerrit Cole, who allowed two runs on six hits in a laborious 4 1/3-inning outing. Cole struck out four and walked four in his shortest postseason outing since lasting two-plus innings in the 2021 wild-card game at Boston.

"I lost a little bit of the zone, a few too many walks again," Cole said. "But I think they threw a lot of quality at-bats together, and ... they won some of those long at-bats, and they ended up putting enough pressure on us that it didn't allow us to continue to cruise."

Cole stranded two in the third inning by retiring Jose Ramirez for the final out and left the bases loaded in the fourth by getting a called third strike with his curveball to Rocchio.

Cleveland pulled within 3-1 on Josh Naylor's sacrifice fly in the fifth, and Cole was replaced by Clay Holmes after walking Lane Thomas to load the bases with one out. Holmes gave up a run-scoring groundout to Brennan, then walked the bases loaded again before striking out Austin Hedges to end the inning.

Cleveland is 0-2 for the first time in its six appearances in the ALCS after Rocchio and Brennan committed run-scoring errors.

"It was what it was," Cleveland manager Stephen Vogt said of Rocchio misplaying Judge's popup. "I think the run would have scored on the next play with the sac fly. It's not ideal obviously to have that happen."

Holmes (2-0) was among four New York relievers who combined to pitch 4 2/3 innings. Luke Weaver allowed a one-out homer to Ramirez in the ninth before closing out the win.

"You know it's coming," Holmes said of Judge's homer. "It's one of those things if he keeps swinging it's going to happen."

Cleveland starter Tanner Bibee (0-1) allowed three runs (two earned) on five hits in 1 1/3 innings. He fanned two and walked one. The Guardians used seven relievers the rest of the way.

--Larry Fleisher, Field Level Media