Rochdale, who sit 12 places above Barnet in the League Two table, were marginally the more threatening side in an instantly forgettable first half.
Lee Thorpe threatened twice from distance early on, while in an almost isolated instance of quality, Will Buckley wriggled to the bye-line and flashed a shot across the face of goal.
The teams were greeted by traditional testing FA Cup weather which seemed to inspire the visitors and they took the lead in the 49th minute.
Gary Jones was allowed far too much time to send in a cross from the right and Chris Dagnall bundled the ball home from unmissable range.
But Ismail Yakubu won his side a replay with a finish his Everton namesake would have been proud of when he collected Nicky Deverdics' deflected free-kick and slotted past Sam Russell.