The Cowboys converted two late Nebraska turnovers into touchdowns to pull within 37-34 with 1:32 left. Nebraska recovered the onside kick after Brett Smith's 47-yard TD pass to Robert Herron.
Wyoming's defense held, and the Cowboys got the ball back on their 6 with 1:07 to play, but time ran out on them before they could even get to midfield.
Martinez completed 17 of 22 passes for 155 yards. Abdullah ran for 114 yards and Cross for 105.
Nebraska needed all 530 of its total yards because Wyoming was able to put up alarming numbers against a defense that had to replace eight defensive starters.
The Huskers never could get comfortable, not even after Ciante Evans' interception at the Nebraska 10 with his team leading by 16 points with less than 10 minutes left in the game.
The Cowboys got the ball back when Blair Burns intercepted Martinez, and Smith's 29-yard touchdown to Jalen Claiborne pulled the Cowboys within 37-27 with 6:02 to play. The Cowboys' 2-point try failed when Smith was sacked by Josh Mitchell.
After Marqueston Huff recovered Martinez' fumble at the Wyoming 38, Smith found Herron along the right sideline for another TD that stunned the crowd on a sweltering night at Memorial Stadium.
The Huskers looked like they would take control after going into halftime ahead 17-14.
Cross scored his second touchdown after he took a handoff, slipped up the middle, bounced off linebacker Jordan Stanton and spun around twice before finishing his 31-yard touchdown run for a 24-14 lead.
Nebraska went 67 yards in 15 plays on its next series, with Martinez lofting a 3-yard touchdown pass to Quincy Enunwa. Officials ruled Enunwa didn't get his foot down inbounds, but the call was overturned on video review.
Wyoming pulled to 31-21 when Brandon Miller caught a short pass from Smith and battled his way into the end zone for a 22-yard TD.
Nebraska has won all seven meetings with Wyoming and is 33-2 against current members of the Mountain West Conference.
The Cowboys went 64 yards in six plays on their second possession to take the early lead. Wick ran 37 yards down the sideline before Smith hit Claiborne with a 6-yard touchdown pass after getting flushed from the pocket.
Another big run, this one a 47-yarder by Smith, helped the Cowboys go up 14-10 early in the second quarter. Harvey Jackson made the touchdown-saving tackle on Smith, but Wick bulled into the end zone from 6 yards three plays later.
Nebraska regained the lead with 5:59 left in the half after Abdullah broke a career-long 62-yard run. He eluded Huff's diving tackle attempt before making it to the corner. He accelerated past Stanton and would have scored if Darrenn White, who had an angle on him, hadn't knocked him out of bounds at the Wyoming 18.
Cross went up the middle for 17 yards and fumbled, but receiver Quincy Enunwa recovered, and Cross went ran into the end zone on the next play for a 17-14 lead.
The game drew a school-record attendance of 91,185, made possible by a 6,000-seat addition to the east side of Memorial Stadium.