Taumua's block on a 35-yard field goal attempt by Thomas Weber came after Kyle Watson kicked a 20-yard field goal on the Rebels' overtime possession.
The loss took the luster off Arizona State's game against No. 2 Georgia next week.
For the Rebels, it will go down as one of the great victories in the school's sometimes checkered football history.
UNLV (2-1) tied it at 20 with 18 seconds left on Omar Clayton's 8-yard touchdown pass to Phillip Payne, who made a leaping one-handed grab.
The spectacular play capped a 10-play, 74-yard drive that lasted 2:45, with Clayton 6-of-8 passes for 70 yards.
For the Sun Devils (2-1), this was supposed to be a tuneup for next week's long-awaited game against No. 2 Georgia. But they let the Rebels hang around for too long.
Arizona State looked safe when Rudy Carpenter hit Kyle Williams for a 49-yard touchdown pass to put ASU ahead 20-10 early in the third quarter.
The Rebels served notice that they weren't going to be pushovers late in the second quarter. Carpenter threw an interception to UNLV defensive back Beau Orth, who returned it 9 yards to Arizona State 7.
Three plays later, Clayton threw a 2-yard touchdown pass to Payne, who outleaped cornerback Omar Bolden in the end zone with 33 seconds to play.
The Sun Devils responded with a quick four-play, 33-yard drive capped by Weber's 49-yard field goal as time expired in the first half, giving ASU a 13-10 halftime lead.
The Sun Devils had vowed that they would not look past the Rebels to next week's long-awaited visit by the Bulldogs - but it certainly looked that way early on.
Arizona State moved the ball easily on its first drive but stalled near the Rebels' goal line, extending a troubling early season trend. ASU had first-and-goal at the UNLV 9, but gained only 6 yards and had to settle for a 20-yard field goal by Weber.
That was a bad sign against a team tied for last in the nation in red zone defense. It was the first time in six attempts this season that the Rebels had stopped a team inside its 20-yard line.
On its next drive, Arizona State didn't come close to the end zone, giving up back-to-back sacks to a team that had one sack through the first two games.
The Rebels tied it at 3-3 on a 44-yard field goal by Watson midway through the second quarter.
Clayton completed 19-of-31 passes for 191 yards and two touchdowns for UNLV, which plays host to Iowa State next week. Carpenter finished 13-of-23 for 242 yards and two touchdowns, and he was intercepted once.
http://accesswdun.com/article/2008/9/213289