After Yankees slugger Aaron Judge led off the second game of the doubleheader against the Rangers with his American League-record 62nd homer, Cole struck out Nathaniel Lowe in the bottom of the first inning.
He would compile 8 more strikeouts over 6 innings pitched, giving him a final total of 257 K's for the season.
"Even just to tie the record, and let alone break it, it's a bit surreal," Cole said. "And obviously on a night like tonight, it's just kind of like, whoa, I mean, what a lot of history going on. Just a wonderful experience to share it with my teammates.''
Cole had four strikeouts in his previous start Sept. 28 at Toronto to match Guidry, whose 248 strikeouts came in 1978, when he was the AL Cy Young Award winner after going 25-3 with a 1.74 ERA.
Guidry (1978-79) and Cole are among only four pitchers in Yankees history with multiple 200-strikeout seasons, joining Luis Severino (2017-18) and David Cone (1997-98). Cole's 243 strikeouts last season are third on the team's single-season list.
The Associated Press contributed to this report.