The Fighting Irish (6-0) got the ball first in overtime and Tommy Rees connected with T.J. Jones on a 7-yard scoring pass, breaking a 13-13 deadlock.
On Stanford's ensuing possession, Josh Nunez guided the Cardinal (4-2) to the Notre Dame 2-yard line, but two tries by Taylor on third and fourth down to punch the ball into the end zone failed.
His fourth-down try was reviewed by officials but they ruled he had not crossed the plane of the goal, keeping the Irish undefeated and giving them an inside track to a bowl game berth.
Rees (4-for-4 passing, 43 yards) relieved an injured Everett Golson on the final drive in regulation and Kyle Brindza forced overtime with a 22-yard field goal with 20 seconds left.
Nunez completed 12-of-25 passes for 125 yards but was picked off twice in the loss.
Taylor ended with 102 rushing yards on 28 carries.