Rico Gathers had 14 points and 15 rebounds for the Bears (13-3, 2-2 Big 12), who had led throughout until Georges Niang made a jumper with 1:54 left for a 68-67 lead.
Baylor had started the game with a 16-1 run, and was up 62-48 on a layup by Gathers with 8:40 left before the big closing surge by Iowa State (12-3, 2-1) that included the back-and-forth finish.
Lester Medford hit a 3-pointer from the right corner with just over a minute left for Baylor, but Iowa State (12-3, 2-1) quickly got even on Niang's high bank shot.
Johnathan Motley had a go-ahead putback on a miss by Chery before the Cyclones went back ahead on a 3-pointer by Bryce Dejean-Jones.
Iowa State called timeout after Chery's last basket, but Niang missed a runner as time expired.
Niang scored 10 points, nine over the final 8 1/2-minute stretch to erase Baylor's 62-48 lead.
Naz Long had 19 points for Iowa State, making all five of his 3-pointers.
Three of Long's 3s came in that late 20-5 run that put Iowa State ahead for the first time. Dejean-Jones has 14 points and Monte Norris 11.
Royce O'Neale led Baylor with 15 points. Motley had 14 and Chery 13.
Baylor led 16-1 lead while hitting four 3-pointers in the first 3:15 of the game, then ended the half with a 12-2 run after Iowa State had gotten within a bucket.
After Matt Thomas missed an open 3 for Iowa State, Gathers had a strong inside basket to start Baylor's half-ending run. O'Neale then had a tip-in of a miss by Chery and had a 3-pointer for a 46-34 halftime lead.
The Bears were up 11-1 after only 2 minutes by hitting their first four shots. Chery hit a 3, then had another long jumper between consecutive 3s by O'Neale. They got it to 16-1 before Iowa State made its first field goal, a 3-pointer by Long more than 3 1/2 minutes into the game.
Iowa State was trying to win its first three road games of a season for the first time since 1987-88.
Baylor's 46 first-half points were the most by halftime this season, and the most given up in any half by Iowa State. ... The Bears had three double-figure scorers by halftime, O'Neale with 11 points, and Gathers and Chery with 10 each.
Iowa State: is home Saturday night against No. 12 Kansas.Baylor: plays Saturday at Kansas State.