“I still feel he’s going even to another level,” Manager Aaron Boone said of Taillon, who is only nine starts removed from his second Tommy John surgery, in 2019 while with Pittsburgh. “I keep being so encouraged by what we’re seeing.”

The Yankees’ starting rotation, which came into the season with several question marks, did some of its finest work against a Chicago team that entered the series averaging 5.3 runs per game, second best in the majors. Montgomery struck out a career-high 11 batters on Friday night, and Cole, the lone Yankees starter who seemed like a sure thing entering the season, silenced the White Sox on Saturday despite not having his best stuff.

It wasn’t just the arms that paved the way.

Gleyber Torres caught fire in the series, hitting a home run and a walk-off single on Friday, driving in four runs on Saturday and smacking a two-run single on Sunday. Torres, whose glove has also looked better at shortstop as of late, has eight R.B.I. in five games since coming off the Covid-19 injured list.

“The first couple weeks of the season was a struggle,” admitted Torres, who was batting .234 before being sidelined. “I didn’t hit really well.

“I feel really well right now. I go to home plate and just try to be simple, try to put the ball in play and help my team.”

Across the board, it has been an unusual stretch for the Yankees. The cluster of breakthrough coronavirus cases, which included Torres, still had the team missing members of its coaching and support staff in Texas. Kluber threw his no-hitter without the pitching coach, Matt Blake, in the dugout. And on Friday, the Yankees became the first team in M.L.B. history to have a no-hitter, a triple play and a walk-off win in a three-day span, per Stats.

The team even survived closer Aroldis Chapman’s allowing his first earned run of the season thanks to Chicago’s gift of loading the bases ahead of Judge’s game-winning walk.