Michael Lee Felder, 35, and Kayla Lauren Miller, 25, both of 9126 Springhill Lane in Greenbelt, were charged overnight with drug possession with intent to distribute, among other drug and gun charges, police said.
Police said searches of both suspects when they were arrested also revealed drugs and drug paraphernalia.
Police were serving the warrant at the motel when they saw a man and a woman drive off in a 2003 Ford Taurus.
When police tried to make a traffic stop, the driver, identified as Felder, refused. Police began the pursuit, which was "on various roadways, through multiple jurisdictions," the release said.
The chase ended on I-95 south near I-695 when Felder stopped the car and both suspects surrendered.
Police said Felder and Miller were arrested without incident, and are awaiting bond hearings at the Howard County Detention Center.