The bombers with explosives strapped to their bodies entered the Jimeta Main Market after sundown yesterday and "pretended to be fighting", said area police spokesman Othman Abubakar.
The staged fight between the two men "attracted the attention of people nearby to see what was happening," he told AFP.
"When people had gathered they detonated their explosives... They killed a sizeable number of people," he added.
The coordinator for the National Emergency Management Agency in Yola, Sa'ad Bello, gave casualty figures of 31 dead and 38 injured.
Yola has also suffered attacks, but not in recent years. It had come to be seen as a relative safe haven for hundreds of thousands of people forced to flee their homes further north because of the violence.
The Yola attack came hours after a suspected suicide bombing at a checkpoint outside a military barracks in Maiduguri, the capital of neighbouring Borno state that killed four people.