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.