Iowa State's Austen Arnaud, scrambling on fourth-and-9, had Darius Darks in the open in the end zone but overthrew him with a minute left and the Jayhawks (5-0, 1-0 in the Big 12) held on.
Reesing was 37 for 49 and tied his own school record with 37 completions. The Jayhawks scored twice in the fourth quarter after the Cyclones (3-3, 0-2) took a 30-27 lead behind Arnaud and Alexander Robinson, who ran for 152 yards and two TDs. Arnaud passed for 293 yards and two scores.
Meier had 16 catches for 142 yards and two TDs, and teammate Dezmon Briscoe had 12 catches for 186 and two more scores.
Meier now holds school records for career receptions and his 16 catches broke the single-game mark he had shared with Briscoe.