The Zips (4-1) built a 62-49 lead with four minutes to play, but that was narrowed to just three when Temple's Luis Guzman made a 3-pointer with 27 seconds left to cap a 13-3 run.
Seconds later, Conyers stepped to the line and sank both free throws to give the Zips a five point cushion. Guzman made a layup and teammate Mark Tyndale made one of two free throws, but it wasn't enough.
Nick Dials scored 16 points and Jeremiah Woods had 14 for the Zips. Conyers added nine points and nine rebounds.
The two teams have only met once on the hardwood, that being an 80-73 overtime win by Akron in the first round of the 2006 NIT at the Liacouras Center. That game was the last in coach John Chaney's 24 years at Temple.