The deputy said he became suspicious after listening to the men's answers and after viewing their behavior, he said.
It was not immediately clear what the men were doing in Nebraska.
Authorities in Lincoln said an investigation into the duo's activities in Nebraska was ongoing.
Laursen said the escapees were facing pending charges in Nebraska and then would be extradited to Utah.
Derrick and Braham had been housed at the Uintah County Sheriff's jail under contract with the Utah Department of Corrections.
The duo fled the Vernal jail Wednesday through a 3-foot-by-2-foot vent of a laundry room where they worked. They then allegedly stole a green 1996 GMC Yukon from a nearby residence. It wasn't clear if they were still in the vehicle when they were apprehended.
Derrick was serving a sentence for second-degree felony burglary, third-degree felony theft, third-degree felony possession and/or use of a controlled substance, third-degree felony failure to stop or respond at the command of police, and class A misdemeanor child abuse.
Braham was behind bars for second-degree felony burglary, second-degree felony theft, third-degree felony theft, third-degree felony burglary and class B misdemeanor theft.