"The two men, who we suspect to be terrorists, were traveling in a Toyota car, which suddenly exploded," Hassan Liman, a local resident and tea seller, told The Anadolu Agency by phone.
"They were traveling in the direction of the Evangelical Church of West Africa in Gombe town," he said.
Audu Bakura, a member of a local vigilante group, confirmed the fatalities.
"They were about to be stopped by security agents when their car exploded," Bakura told AA.
"Our suspicion is that the militants – in a bid to escape security vetting – set their explosives to go off if they encountered a breach in their plan," said the local vigilante.
The incident occurred one day after an explosion – described as a failed suicide bombing attempt – went off inside a Gombe market.
The death toll from the Wednesday evening blast remains uncertain.
Neither the police nor the army has spoken on either incident.
Also on Wednesday, six suspected militants were killed in Fika, a major town in Nigeria's northeastern Yobe State, when their vehicle – which was apparently laden with explosives and headed to Damaturu, the state's provincial capital – exploded.
Police confirmed the incident, but did not provide a death toll.
The army on Wednesday announced a curfew across several northeastern towns in a bid to curtail the activities of Boko Haram militants who they fear could be plotting holiday attacks.
For the last five years, Nigeria has battled a fierce Boko Haram insurgency that has ravaged the country's volatile northeastern region and claimed thousands of lives.
2014 proved to be the insurgency's bloodiest year yet, with increasingly frequent attacks, higher death tolls and a deluge of displaced persons.
A seemingly emboldened Boko Haram recently stepped up its militant activity, seizing several areas of Nigeria's Adamawa, Borno and Yobe states, where it has since declared a self-styled "Islamic caliphate."