Hope Akpan's first goal for Crawley earned his side a draw with Accrington as they dropped to second in the table.
Stanley made the breakthrough just before half-time when Peter Murphy converted from close range.
Substitute Akpan then equalised after he drilled in a powerful shot from the edge of the area.
Michael Doughty had a late chance to win it for Crawley but saw his dipping shot tipped onto the crossbar by Dunbavin to keep the scores level.
Crawley are now behind Southend on goal difference.
VIEWS FROM THE DRESSING ROOM
Crawley boss Steve Evans told BBC Sussex:
"We're disappointed. That would finish football, having to play against that every week.
"We started on the back foot and didn't really get going. Credit to our players, we gave it our best in the second half.
"Their only shot is the goal. They didn't try to play. It's two points dropped. We'll get back on the training ground on Monday and work hard."