Taylor carried the ball 20 times and scored one of two first-period touchdowns for the Cardinal (12-2), which sealed the victory when Usua Amanam intercepted a Curt Phillips pass with 2 minutes remaining.
Kevin Hogan completed 12-of-19 passes for 123 yards and Kelsey Young ran for a score for Stanford, which won its first Rose Bowl since 1972.
Montee Ball rambled for 100 yards with a touchdown on 24 carries for the Badgers (8-6), who were appearing in the post-season game due to NCAA bans on Big Ten conference champion Ohio State and Penn State.
He became the first player in NCAA history to score TDs in three different Rose Bowls.
Wisconsin Athletic Director Barry Alverez led the squad in the absence of former Coach Bret Bielema, who left for Arkansas last month.