The Huskers (4-0) rolled up 490 yards total offense, including 333 on the ground, in their first road game of the season and last game before their highly anticipated Big Ten opener at Wisconsin next weekend.
Burkhead had TD runs of 45 and 16 yards, piling up the yards on just 15 carries. His previous career high was 129 yards against Iowa State in 2010.
Wyoming (3-1) was led by quarterback Brett Smith, who passed for 166 yards and two scores. The Cowboys entered the game with its first 3-0 start since 1996, although two of their games this year were against lower-division FCS teams and they struggled with Nebraska.
The Huskers scored on their first two possessions of the second half and opened a 31-7 lead on Burkhead's 16-yard scamper, a 20-yard field goal by Brett Mahar and an 8-yard TD pass from Martinez to Kenny Bell.
Smith connected with Robert Herron on a 10-yard TD pass, only to see Nebraska drive for a score on its next possession on a 1-yard run by Braylon Heard.
Wyoming, which entered the game averaging 36 points and 492.3 yards of offense, were held to 305.
Nebraska led 14-7 at halftime. Burkhead scored on his second carry of the game, romping 45 yards off the left side on first down. Martinez followed with an 8-yard TD run up the middle before Wyoming answered with a 48-yard TD pass from Smith to Mazi Ogbonna, who took a short slant pass and avoided three Nebraska tacklers as he cut across the field.
Nebraska star defensive tackle Jared Crick did not suit up for the game after suffering an unspecified injury the week before against Washington. The 6-foot-6, 285-pound senior had started 31 straight games for Nebraska. He has 14 tackles and one sack in three games this season.
Nebraska cornerback Alfonzo Dennard played in his first game of the season after pulling a muscle in his right leg in mid-August. He sat out most of the second half, finishing with four solo tackles.
It was Nebraska's first road game at a non-BCS conference school since a 38-14 win in 2003 at Southern Miss., and the first time the Huskers had visited Laramie even though the two states border each other. The game drew 32,617 people to War Memorial Stadium, making it the third-largest population center in Wyoming on Saturday. Many were wearing Nebraska red.
The stadium has a listed capacity of just about 29,200, which the smallest stadium Nebraska has played in since 1971.