Those same fans might have been biting their fingernails and getting sweaty palms when a four-run lead turned into a two-run advantage and threatened to turn into a deficit.
Not left-handed reliever Tommy Layne.
"If you try to change how you throw because you got guys on and let the situation put pressure on you, that's when you typically fail," Layne said. "For me I approach it as more of a free and easy because that's when you're at you're best.
Tanaka (12-4) gutted through 6 1/3 innings but when pinch-hitter Dioner Navarro launched a fly ball to the warning track that Judge hauled in, Yankees manager Joe Girardi sprinted to the mound for the first of three pitching changes in the inning.
With normal seventh inning man Adam Warren unavailable, Jonathan Holder was the first to get a call. He recorded the second out but made losing the lead more of a possibility by walking sluggers Jose Bautista and Josh Donaldson to load the bases. Then came Ben Heller, who got beat with his fastball for a two-run single by Edwin Encarnacion.
Layne was next and he originally was supposed to face left-handed hitting Michael Saunders with runners at first and third. He was prepared for another hitter and instead faced right-handed hitting Martin, who came in with a .338 average over his last 18 games.
The inning ended with a full count curveball that Layne got Martin to harmlessly hit into second baseman Starlin Castro's glove in short right field.
"I do a lot of work on scouting reports, so I kind of have an idea of what do before I get out there," Layne said. "It's a matter of executing pitches."
After the seventh-inning escape, Tyler Clippard pitched a hitless eighth and Dellin Betances did the same in the ninth for his ninth save.
"I believe in them," Girardi said. "I believe that they can get outs. Holder got a big out for us and Tommy Layne had to finish it up. I thought Heller made a good pitch. I believe in these kids and they're going to get more comfortable and you have to keep throwing them out there."
Layne was not the only Yankee (71-65) to execute on a day when they remained 3 1/2 games behind Baltimore for the second wild card spot.
Jacoby Ellsbury hit a two-run home run off R.A. Dickey (9-14) and tied a season-high with three RBIs while rookie first baseman Tyler Austin had a two-run double in the fourth. Those runs ultimately proved to be the winning runs.
The Yankees also made some strong defensive plays. Besides his catch at the wall, Judge also made a diving catch on Travis for the final out of the second.
Austin threw out Jose Bautista at the plate after he drove in Toronto's first run in the first.
Catcher Gary Sanchez threw out Melvin Upton Jr. trying to steal second in the fourth in a two-run game and left fielder Brett Gardner threw out Bautista at third after the Yankees took a four-run lead.
Toronto lost for only the fifth time in its last 16 trips to New York but has dropped four of its last six. The Blue Jays were held without a home run for the third time in four games and were 2-for-9 with runners in scoring position.
"We made a run at it, we got close, couldn't add anymore," Toronto manager John Gibbons said.
Dickey allowed five runs and seven hits in four innings. The veteran knuckleballer fell to 0-6 at New York since being acquired from the New York Mets following the 2012 season.
"They hit Dickey around today a little bit," Gibbons said. "We scored and then they came right back with a two-run homer to take the lead. I thought he was a little inconsistent with the knuckleball today."
Toronto took a quick 1-0 lead when Bautista singled to right field and appeared poised for more when Encarnacion singled with one out. Bautista was thrown out at the plate by Austin on a ground ball by Saunders and Tanaka retired Kevin Pillar.
The Yankees never trailed after Ellsbury sent the first pitch from Dickey into the right field seats for his seventh home run. Two innings later, Austin led off with a double and scored on Ellsbury's single.
The lead reached 5-1 with two outs in the fourth. After Judge struck out, Austin roped a two-run double off the left field wall.
NOTES: Toronto SS Troy Tulowitzki is 0-for-7 lifetime against New York RHP Masahiro Tanaka and was given the day off. ... New York has not announced a starting pitcher for Wednesday but RHP Bryan Mitchell could be an option if the Yankees do not opt for a "bullpen game." Mitchell has 14 strikeouts in nine innings in two starts with Triple-A Scranton/Wilkes Barre and has made six minor league starts after missing four months with a toe injury. ... New York 1B Greg Bird (torn labrum) has progressed well enough to the point where is taking batting practice in the batting cage. If he doesn't haven setbacks with his shoulder or other injury, Bird is expected to face live pitching in the instructional league this month and during the Arizona Fall League. ... RHPs Bo Schultz and Aaron Loup are expected to join Toronto on Tuesday.