The chase began when National Security Agency officers attempted to pull over Darnell David Hawkins, Jr.'s dark-colored SUV on a traffic stop along Route 32 just before 6 a.m., authorities said.
The highway cuts through Fort Meade, where the NSA campus is located, and is near the casino.
After initially coming to a stop, police said Hawkins then accelerated and fled from the scene.
Maryland state troopers joined NSA officers in the pursuit near West Nursery Road after they said they spotted Hawkins vehicle driving northbound in the southbound lanes of the Parkway.
After about 15 minutes, authorities managed to capture Hawkins when the tires on his SUV blew out.
Neither Hawkins or troopers were injured during the pursuit, but an NSA officer suffered minor injuries.
Hawkins was charged with attempting to elude police; a motive for the chase was not immediately known, authorities said.