The Huskers (10-2, 7-1 Big Ten) will face off against Wisconsin next Saturday in Indianapolis. It'll be a rematch of Nebraska's thrilling 30-27 home win over the Badgers in late September.
Burkhead, making his first appearance since aggravating a sprained left knee on Oct. 20 against Northwestern, broke through with a 3-yard TD run to make it 13-7 late in the third quarter.
Alonzo Whaley's interception with 2:11 left sealed the victory for Nebraska.
The Huskers defense held the Hawkeyes (4-8, 2-6) scoreless in the final three quarters in windy conditions.
Mark Weisman had 91 yards rushing for Iowa, which finished the season on a six-game losing streak. The Hawkeyes will miss out on a bowl game for just the second time since 2000.
Nebraska's offense spent much of the day stifled by a stiff wind that gisted up to 40 mph and a surprisingly stout Iowa defense.
Fittingly, quarterback Taylor Martinez and Burkhead teamed up to put the Huskers ahead.
Martinez beat quadruple coverage for an 18-yard completion to Braylon Heard, an impressive hookup considering the conditions. Burkhead was in the end zone a few plays later to make it 13-7 with 3:10 left in the third quarter.
Iowa pinned Nebraska at the 1 with 12:03 left, but Burkhead willed the Huskers out of harm's way with runs of 9 and 8 yards into the wind.
Though the Huskers were later forced to punt, Burkhead helped them avoid the worst while burning valuable minutes off the clock.
Burkhead finished with 69 yards rushing - all in the second half.
A mild fall in the Midwest came to an abrupt end on Friday.
During the national anthem, the breeze at Kinnick Stadium was so strong it nearly blew over the American flag - and the man holding it. The wind chill hovered in the teens all day.
The conditions made passing a risky venture. Martinez threw for just 63 yards, while Iowa's James Vandenberg had 92 yards passing and two picks.
Nebraska threw just once on a 16-play drive that led to a field goal, and Iowa did the same on a 62-yard drive that led to a 1-yard plunge from Vandenberg and a 7-3 lead it held at halftime.
The Huskers muffed a punt and Martinez fumbled and nearly threw a pick in the second quarter. But Iowa's offense, which was lackluster all season, couldn't turn those miscues into points.
The year-long ineptitude of Iowa's offense reached its nadir late in the first half. They were penalized for having too many men on the field - even though they were coming out of a timeout - and Mike Meyer followed with a missed field goal.
The Huskers had the wind at their backs to start the second half, allowing Brett Maher to nail a 52-yard field goal.
Nebraska finished with a 7-1 conference mark for the first time since 2001, when it posted the same mark in the Big 12.
With one more Big Ten win next weekend, Nebraska is headed to the Rose Bowl.