Up seven at the break, ISU jumped ahead 47-32 with a 14-6 run. Taylor, known primarily as a scorer, set a career high with eight assists - two of which keyed the decisive run. He found Johnson for two with a perfectly placed lob, then hit Hubalek with a no-look pass under the basket.
Taylor hit a three to give ISU its biggest lead, 52-36, with 12:05 left.
Baylor chipped away at the Cyclones' lead, and got within 65-58 on a 3-point play by Kevin Rogers with 2:17 to go. ISU's Corey McIntosh answered with a layup on the other end, and Baylor turned it over on its next possession. Hubalek then hit a floater in the lane and a free throw to seal the win.
Johnson picked up his 11th double-double, breaking the school record for a freshman. He is now tied with Texas freshman Kevin Durant for the most double-figure rebounding games by a Big 12 player with 13.
ISU went on an early 14-2 run - highlighted by a fast-break tomahawk dunk from Johnson - and led 33-26 at halftime.
The win helped the Cyclones avoid their longest Big 12 losing streak since 2002, when they dropped eight in a row.
Baylor extended its road losing streak to 22 games dating back to 2004.