The 18-year-old Culbreath, who has represented Germany and the United States at youth level, came off the bench in the 77th minute. With Leipzig searching for an equalizer, Culbreath surged up the field on a stoppage-time breakaway and scored into the top-left corner, wheeling away with arms wide in celebration.
Culbreath then had to wait to learn if his goal would count as VAR checked Leipzig's claim of handball in an earlier incident at the other end.
While he previously represented the U.S. at U16 level, Culbreath has most recently appeared for Germany's U19 team.
Leverkusen enters the winter break third in a season which began in chaos when Erik ten Hag was fired as coach after three games. Kasper Hjulmand has overseen nine wins in 13 Bundesliga games since.
Leverkusen dominated early on but Leipzig opened the scoring through Xaver Schlager's low shot fromthe edge of the box after the defense was slow to react at a throw-in.
Martin Terrier leveled five minutes later with a header from Arthur's cross, and Patrik Schick scored Leverkusen's second near halftime, leaving a defender sprawling and lofting the ball over the goalkeeper.
Leverkusen held on to inflict Leipzig's first home loss of the season despite missing left back Alejandro Grimaldo, center back Edmond Tapsoba and attacking midfielder Ibrahim Maza due to injury or the Africa Cup of Nations.
Leverkusen climbed to third, dropping Leipzig to fourth. Bayern Munich leads by six points from Borussia Dortmund and plays Heidenheim on Sunday.
Information from The Associated Press was used in this report.
