Third-seeded Ohio State, which ended the regular season ranked ninth, trailed by two at the half but saw the second-seeded Cardinal methodically build a double-digit lead in the first seven minutes of the second half in front of 6,178 at Haas Pavilion.
That sent Lavender to the bench, but the Buckeyes (29-6) remained game for a while.
OSU point guard Samantha Prahalis made two free throws and then a pull-up jumper to begin a 10-4 run that pulled the Buckeyes within three at 57-54, but then Appel made a hook shot to push the deficit back to five.
After Sarah Schulze made a free throw for Ohio State, the Cardinal scored six in a row to go back up by 10 before the Buckeyes' last significant thrust.
Schulze made a layup then the Buckeyes made 5 of 6 free throws to draw within four at 66-62 with 5:39 to go.
After a defensive stop, Ohio State had a chance to make it a one-possession game, but Allen threw the ball away for a turnover.
At the other end, Appel scored to push the advantage back to six, and the Cardinal scarcely looked back: Stanford finished the game on an 18-4 run.
That the first 35 minutes were so closely contested was largely a testament to the talent and tenacity of Prahalis, who willed the Buckeyes to basket after basket, whether she was driving to the basket, hitting pull-up jumpers with unusual efficiency or finding her teammates for scores.
The freshman phenom finished with a team-high 19 points, six assists and two steals.
Lavender, the two-time Big Ten player of the year, was limited to 28 minutes because of foul trouble and posted 15 points.
Bettering her was Appel, her 6-4 counterpart at center for the Cardinal who finished with a game-high 25 points and 11 rebounds.
Perhaps more importantly, Appel got support in the frontcourt from 6-1 forward Jillian Harmon (16 points) and 6-2 Nnemkadi Ogwumike (15 points).
Down the stretch, the Cardinal buried the Buckeyes in the paint, and Ohio State could not offset their disadvantage there with bombs from the perimeter.
Ohio State missed 7 of 10 three-point attempts, getting all three makes from sophomore Sarah Schulze, who came off the bench to score 12 points.
She had two of those treys in the first half, the second being the first basket in a five-point mini-run that allowed Ohio State to briefly take a one-point lead.
Prahalis followed Schulze's trey with a pull-up jumper to put the Buckeyes ahead 31-30 with almost four minutes left before halftime.
Next the OSU point guard appeared to extend the lead to three after she made a steal and raced to the other end. She made a layup and collided with solidly built 6-4 Stanford forward Kayla Pedersen under the basket, but while the official nearest the play signaled a blocking foul on Pedersen, the one trailing the play from a greater distance whistled an offensive foul on the 5-7 Prahalis.
That wiped out the basket and sent Prahalis to the bench with her second foul and 3:36 left in the half.
By that time, Prahalis had scored 12 points and handed out three assists while looking perhaps more aggressive than she had all season.
The teams traded the lead six times in the last 3 1/2 with the Cardinal taking a 37-35 lead into the locker room thanks to a deep trey by Lindy La Rocque with just under a minute to go.
Stanford, the national runner-up last season, improved to 32-4 and extended its winning streak to 19 games.