The Cornhuskers (3-1) led 35-0 after the first quarter and 45-0 at half.
The Bengals (1-2), of the Football Championship Subdivision, have lost 34 straight road games and 46 of their last 52 games overall.
Burkhead, playing for the first time since he sprained his left knee in the opener, broke a 61-yard touchdown run on his third carry. His 2-yard TD on his eighth and final run early in the second quarter made it 42-0.
Nebraska also got touchdowns on Ciante Evans' 29-yard interception return and Ameer Abdullah's 81-yard punt return, making it the first time since the 2009 game against Colorado that the Huskers scored on offense, defense and special teams.
Idaho State's score came on CJ Reyes' 28-yard pass to Luke Austin in the fourth quarter.
Nebraska rushed for 385 of its 569 total yards.
Freshman Imani Cross had 100 yards and a touchdown on 12 carries, all in the second half.
Idaho State had 210 total yards, all but 72 coming in the second half against Nebraska's defensive reserves. Kevin Yost was 16 of 34 for 123 yards, with two interceptions. He was sacked six times.
Nebraska coach Bo Pelini was back on the sideline. He became ill during last week's game against Arkansas State and was taken to a hospital by ambulance after halftime. He complained of heartburn and disorientation. A series of tests were negative, and he was back at work the next day.
Idaho State earned a $600,000 guarantee for playing the game, or 5 percent of its $12 million athletic budget.
Burkhead showed no sign of being limited by his left knee. He picked up 6 and 12 yards on his first two carries, then followed left guard Seung Hoon Choi to the outside and broke free from cornerback Phil Pleasant's grasp on his way to the longest run of his career.
Next came Abdullah's 8-yard TD run and Martinez's perfect 35-yard strike to Quincy Enunwa. Then Martinez was credited with a 68-yard TD pass after he flipped the ball a couple feet in front of him to Kenny Bell, who came in motion in front of the quarterback to start his trek down the left sideline.
Evans stepped in front of Yost's pass for Cam Richmond and ran to the end zone untouched for a five-touchdown lead.
Nebraska's 45 points in the first half were its most since scoring 52 against Baylor in the first half in 2000.
The Huskers scored again when Abdullah fielded Reyes' bouncing rugby-style punt at his 19-yard line, made three defenders miss and cut inside near the goal line as blocker Daniel Davie kept Donovan Henley at bay.
Martinez completed 9 of 13 passes and moved into fifth place on Nebraska's career passing list with 4,598 yards, overtaking 2001 Heisman Trophy winner Eric Crouch.
With his 12th career 100-yard game, Burkhead went from 11th to seventh on the Huskers' career rushing list with 2,841 yards.