Freshman Wesley Johnson added 14 points and 10 rebounds for the Cyclones (12-10, 3-5 Big 12), who blew the game open by hitting eight of their first 11 shots in the second half.
Up seven at the break, Iowa State 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 Iowa State 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. Iowa State'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.
Iowa State 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.