Judge broke open a tight game with his two-run blast in the seventh inning as the Yankees grabbed a 2-0 lead in the best-of seven series, which continues on Thursday in Cleveland.
"We've got to keep things the same," Judge said. "It's going to be a loud environment, a fun environment. We've got to go out there and keep playing our game... feed off the energy and go from there."
The series winner advances to the World Series against either the New York Mets or Los Angeles Dodgers.
Yankees slugger Judge, whose 58 regular-season homers led MLB, crushed a blast over the centerfield wall to give New York a 6-2 lead with his 14th career playoff homer.
"It was good to add two more runs there," Judge said.
The Guardians stranded 11 base runners as four Yankees relief pitchers baffled Cleveland after starter Gerrit Cole went only 4 1/3 innings.
"These guys came in, they're healthy, they're feeling great, some great performances from quite a few guys at the back end," Judge said of New York's relievers.
The Yankees seek their first trip to the World Series since winning it for the record 27th time in 2009 while Cleveland have not reached the event since 2016 and last won a World Series in 1948.
New York's Gleyber Torres doubled down the left-field line, took third base on a Juan Soto single and scored the first run in the opening inning when Judge reached base on an error by Guardians shortstop Brayan Rocchio.
In the second, Anthony Volpe singled, took third on an Anthony Rizzo single and scored on Alex Verdugo's double down the left-field line to put the Yankees ahead 2-0.
Soto was then intentionally walked to load the bases for Judge, whose sacrifice fly off relief pitcher Cade Smith scored Rizzo for a 3-0 lead.
Cole escaped a bases-loaded jam in the fourth by striking out Rocchio, whose third-inning single had given him hits in his first six playoff games to set a Cleveland record.
The Guardians loaded the bases again in the fifth when Steven Kwan singled, stretching his club-record hit streak to 12 games, Kyle Manzardo singled and Jose Ramirez walked.
Naylor drove home Kwan on a sacrifice fly and advanced Manzardo to third. Lane Thomas walked to load the bases again and Will Brennan hit into a fielder's choice that scored Manzardo to make it 3-2 before Yankees reliever Clay Holmes struck out Austin Hedges to end the threat.
The Yankees padded their lead to 4-2 in the sixth when Volpe walked and Rizzo doubled to right field, with Volpe scoring on a throwing error by Cleveland right fielder Brennan, setting the stage for Judge's homer.
Cleveland's Ramirez added a solo homer in the ninth to trim the final margin of defeat.
The Guardians dropped game-one pitcher Alex Cobb from the roster due to a lower left back strain, ending his season. Pitcher Ben Lively was added to the lineup.