Cole surrendered just four hits and one run and did not issue a walk over seven innings in the 116-pitch effort Wednesday at Angel Stadium.
"I thought I was unpredictable and able to use the fastball and challenge guys over the plate once we got the lead, so that was helpful," Cole told reporters.
The win helped the Yankees snap a four-game losing streak.
"That's what we needed out of our ace, especially after the last couple of games," Judge told reporters. "We were just not getting the job done."
"He is our guy," Judge said of Cole. "That's who we want on the mound in a situation when we need to come out with a win. He showed it.
"All of his pitches were working. His fastball was up to 100 mph in the last inning. His offspeed pitches were working. I felt like he was in control the whole game. It was just complete domination."
The Yankees rallied with two outs to score their first run in the third inning. Angels starter Packy Naughton retired shortstop Andrew Velazquez and center fielder Brett Gardner on groundouts to start the frame. Naughton then walked Yankees second baseman D.J. LeMahieu.
Yankees first baseman Anthony Rizzo followed with a line drive single, which sent LeMahieu to third. Naughton issued another walk to Judge in the next exchange. Voit hit Naughton's next pitch -- an 82.1-mph changeup -- into center field for an RBI single.
Gardner plated third baseman Rougned Odor from second base with an RBI single in the fourth exchange of the top of the fourth.
The Angels put their first run on the scoreboard in the bottom of the sixth. Shortstop Jack Mayfield led off the inning with a single to left field. Second baseman David Fletcher doubled off Cole in the next at-bat, which brought in Mayfield and made the score 3-1.
Judge brought in the final run of the day with a 397-foot leadoff homer to left in the eighth.
Naughton allowed six hits and three runs in 3 2/3 innings to drop to 0-1 this season. Fletcher went 2 for 4 with an RBI in the loss.
The Yankees (77-56) remain in first place in the American League Wild Card standings. They host the Baltimore Orioles in the first game of a three-game series at 7:05 p.m. EDT Friday at Yankee Stadium in New York City.
The Angels (66-68) start a four-game series against the Texas Rangers at 9:38 p.m. EDT Friday at Angel Stadium.