Marshall poured in eight points in the second overtime, including two 3-pointers in the final minute and a half.
After Marshall gave the Sun Devils a 67-66 lead, Arizona point guard T.J. McConnell drove the lane and attempted a scoop shot that was swatted by center Jordan Bachynski, the NCAA leader in blocked shots.
Arizona (23-2, 10-2) had a chance to win at the end of the first overtime, but Johnson missed a step-back 18-footer, with the ball going out of bounds to Arizona State with 1.8 seconds left. Carson got off a half-court short at the buzzer, but it was not close.
Arizona State, which has won six of its past seven games, led 51-46 with 2:38 to go in regulation, but Gordon completed a three-point play to bring the Wildcats within two. After each team missed shots, a steal by Arizona forward Rondae Hollis-Jefferson led to a tying layup by McConnell with 47 seconds to go.
Arizona State squandered its chance for the lead when too much dribbling from Carson led to a shot-clock violation. Arizona had about 11 seconds left for the final shot, but Gordon drew air after a spin move in the lane.
Defenses dominated the game early. By the second media timeout, the teams had combined to make 5 of 20 shots from the field and were 0 of 4 from the free throw line.
Scoring picked up from there, with the Wildcats finishing with something of a flourish, scoring 13 points in the final 5:18. Johnson, who was scoreless until that point, had nine points in the half-ending run.
Marshall, the team's second-leading scorer (15.6 points per game) who missed the season's first game against Arizona because of a groin injury, kept the Sun Devils close in the first half with 12 points.
Arizona has taken its largest lead of the half at 20-14 with 3:51 to go on Tarczewski's jumper, but Marshall responded with a 3-pointer and a jumper on the following possession.
Johnson ended the half with a driving layup with five seconds left to give Arizona a 26-21 lead.
NOTES: The in-state matchup produced the first sellout of the season at Wells Fargo Arena. ... Arizona State center Jordan Bachynski entered the game as the NCAA's leading shot-blocker with 4.46 per game. ... With his ninth point on Friday night, Arizona junior guard Nick Johnson passed former center A.J. Bramlett and former guard Gilbert Arenas (1,105 points) for 39th place on the school's career scoring list. ... The Wildcats played their third full game without forward Brandon Ashley, who is out for the season with a foot injury. Ashley, who underwent surgery this week, had 10 points and five rebounds against ASU earlier this season. ... Arizona had at least four current NBA players in the building -- Chase Budinger, Jerryd Bayless, Derrick Williams and Solomon Hill.