Cole (4-1, 1.43 ERA) is scheduled to start against the Los Angeles Angels on Tuesday night at Angel Stadium, about three miles from where he went to high school.
His only other appearance in Anaheim came with the Pittsburgh Pirates on June 21, 2013, the third game of his major league career. He allowed two runs and four hits in 6 1/3 innings of a 5-2 win, and would go on to become the first Pirates pitcher since 1907 to win his first four starts.
After five seasons with the Pirates, Cole was traded to the Astros this past offseason, and he has strung together another strong start with his new team.
He comes in second in the majors in earned run average behind teammate Justin Verlander, the scheduled starter for Wednesday's series finale.
"He's got the ability to stay competitive in the mid-90s and then reach back for the high 90s," Houston manager A.J. Hinch told reporters after Cole allowed one run and four hits in six innings in a 4-1 win against the Oakland A's on Wednesday. "There's a single digit on your hand (for) how many guys can do that."
Cole took his only loss of the season against the Angels on April 23, however, allowing two runs and four hits in seven innings. He was outperformed by Los Angeles left-hander Tyler Skaggs, who threw seven shutout innings in the 2-0 victory.
Cole will be opposed this time by rookie right-hander Jaime Barria.
Barria (3-1, 2.45) hasn't allowed more than two runs in any of his first four career starts this season.
In his toughest test so far, he blanked the Colorado Rockies for 5 1/3 innings on Wednesday, and the bullpen maintained the shutout in the 8-0 victory.
His teammates are impressed by what they've seen so far.
"You don't see a lot of young guys come up here and fill the zone up like he does," Angels infielder Zack Cozart told Fox Sports West. "That's the ultimate key in pitching is throwing a lot of strikes, and once you establish that, you can start working your way out of the zone."
The Angels (25-16) received a strong start from left-hander Andrew Heaney in a 2-1 win in the series opener on Monday night, pulling even with the Astros (26-17) atop the AL West standings.
Angels right fielder Kole Calhoun is hitting just .158, but the former Gold Glove winner has remained stellar in the field. He reached into the stands to catch a fly ball in the ninth inning on Monday, then threw out George Springer trying to advance to second base.
"He's such a gamer and he knows it's important what he does in right field for us," Angels manager Mike Scioscia told reporters after the game. "He's going to help us any way he can. He's working hard, almost too hard on the offensive end. Kind of taking baby steps, but that's not going to affect what he does on defense."
It was the second straight 2-1 victory for the Angels, who edged the Minnesota Twins on Sunday behind another rookie right-hander, Shohei Ohtani.
The Astros, meanwhile, have not allowed more than two runs in their past seven games and Cole should have plenty of incentive to keep that streak alive.