Early in the second half with Ohio State trailing 45-44, Lavender was sitting on 19 points in the game and 2,577 for her career, one shy of the record Katie Smith established 15 years ago.
Ohio State pushed the ball up the floor, Tayler Hill found Lavender wide open under the basket, and the senior from Cleveland cashed in the record-breaking layup for two of the easiest points she has ever scored.
There was no time to celebrate, however, as the Gophers (11-14, 3-9) proved plenty resilient in front of 5,645 fans at Williams Arena.
With less than three minutes to go, Minnesota forward Kristen Dockery tied the game at 71 with a layup.
The Gophers then elected to fall back into a zone to protect the paint, and Ohio State (15-9, 6-6) made them pay.
Hill, who played point guard for nearly all of the second half, brought the ball up and passed inside to freshman center Ashley Adams, who quickly kicked the ball back out to a wide-open Samantha Prahalis on the wing.
Prahalis, the team's usual point guard, buried a three-pointer to put the Buckeyes on top for good.
Adams showed up again at the other end of the floor seconds later as she stepped out to deflect a Konna Kellogg shot on the perimeter.
From there, the Buckeyes closed the game out by making 9 of 10 at the free throw line.
Hill was 6 for 6 from the charity stripe in the final 1:35 while Adams went 3 for 4.
Lavender, who also set an NCAA record by scoring in double figures for the 126th consecutive game, finished as the game's high scorer. She had 29 while Hill had 19.
Hill also handed out seven assists and made three steals. She committed one turnover while playing the full 40 minutes in her hometown of Minneapolis.
Adams notched a double-double with 13 points and 10 rebounds while Prahalis added 11 points and eight assists.
Ohio State forced 16 turnovers and committed only seven.
Kiara Buford repeatedly hurt the Buckeyes with fearless drives to the basket to draw fouls and finished as Minnesota's leading scorer. She had 23 points and went 10 for 14 from the free throw line.
Katie Loberg added 18 points from the post and Voigt had 17 for the Gophers.