The Yankees wound up with an AL wild-card spot Saturday, beating Toronto 2-1 on Judge's 52nd home run shortly before Boston clinched the AL East crown.
New York needed two wins and two losses by Boston to force a tiebreaker Monday at Yankee Stadium. Instead, the Yankees will host Minnesota in the wild-card game Tuesday.
"I started thinking about that the last couple of days where in a sense they're elimination games for us," Girardi said. "We were five down coming home from the road trip and our guys just continued to play well. They continued to play loose. They continued to make pitches, grind out at-bats and that was encouraging to me because it's not like we've had a chance to turn it off and I like that."
The wild-card winner will face Cleveland in the best-of-five AL Division Series. Boston, which beat Houston about 20 minutes after the Yankees won, is set to take on the Astros in the playoffs.
Replacement starter CC Sabathia (14-5) won his fifth straight decision. With the Yankees still in contention for the division title to begin the day, Girardi opted for Sabathia to pitch on his regular four days' rest in place of the originally scheduled Jaime Garcia.
The veteran left-hander didn't disappoint, allowing four hits and striking out six over 5 2/3 shutout innings. The Yankees (91-70) improved to a season-high 21 games over .500.
Sabathia's only close call came with one out in the sixth, when Ryan Goins lifted a fly to deep right that was snagged by a fan reaching over the wall. The initial ruling on the field was interference, which was challenged and upheld after a 38-second review.
Sabathia is 5-0 with a 2.91 ERA in eight starts since returning from the DL on Aug. 19. His 237 career wins put him ahead of Whitey Ford for sole possession of 16th place among left-handers on the all-time list.
Aroldis Chapman pitched a perfect ninth for his 22nd save in 26 chances. The Cuban fireballer has not allowed a run in 11 appearances this month.
Judge hit a drive estimated at 484 feet in the fourth, the shot landing on a walkway behind the left-field bleachers. Judge leads the AL in home runs, and tied Mickey Mantle (1956) for eighth place on the club's single-season list.
"Oh gosh, the ones he hits," Toronto manager John Gibbons said. "I mean, you sit there and admire some of the distance on some of those things."
It was the rookie slugger's 33rd homer at Yankee Stadium, passing Babe Ruth (1921) for the highest single-season home total in franchise history. Judge is 6 for 12 against Marcus Stroman (13-9) with three home runs.
"I've never played for a team like this. Everyone gets along," Judge said. "That's what championship teams are made of, so I'm excited about what's going to happen here in the postseason."
Toronto scored in the eighth on Donaldson's sacrifice fly.
Yankees: Judge was in the lineup at DH, which Girardi considered a half-day off. He planned on giving Judge a full day of rest at some point, but hadn't gotten an opportunity with the club still trying to catch Boston. Girardi said after the game that he plans to sit some of his regulars Sunday.
Blue Jays: LHP Brett Anderson (4-4, 6.97 ERA overall with Toronto and the Cubs) is winless in six career starts against New York.
Yankees: LHP Jordan Montgomery (9-7, 3.96 ERA) will make his 29th start of the season, fifth most by a rookie in team history.
The Yankees spent the night at Dulles Airport after their flight to Kansas City for a series against the Royals was delayed for close to 12 hours. With no hotels available, the players waited in the terminal or slept on the plane.
Buster Olney expects Mike Trout to continue his steady rise as he keeps getting better year after year.
The Brewers put Ryan Braun on the disabled list because of the back tightness that has kept him on the bench for the past three games. Braun is hitting .222 with five home runs and 20 RBIs this season.
Justin Turner tied a career high with five RBI and Kenta Maeda pitched eight sharp innings to help the Los Angeles Dodgers snap a six-game losing streak by beating the Miami Marlins 7-0 Thursday afternoon.
The Cardinals are "hitting the pause button" with pitcher Adam Wainwright and moving him to the 60-day DL because of persistent pain in his right elbow.
Yasiel Puig hits a homer to left field to extend Los Angeles lead over Miami to 4-0.