The visitors grabbed an early lead, then hung on as goalkeeper Ian Dunbavin pulled off several fine saves - including two penalty stops - before Matt Hamshaw finally hauled the Stags level in the 58th minute.
That set up a frantic finale, with substitutes Romauld Boco and Andrew Mangan close to a winner for the visitors before Michael Boulding struck for the Stags in the 81st minute, breaking clear of the offside trap and lifting his finish over the advancing keeper.
However, brave Accrington refused to be beaten and Mullin ghosted in unmarked to head in an Andy Todd free-kick five minutes from time.
Mansfield had an early effort ruled out for offside, despite it being visiting defender Leam Richardson who got the final touch, before Todd and Gary Roberts combined for Mullin to head Stanley in front.
Dunbavin made a point-blank save to deny Richie Barker, before saving a penalty from the same player with his legs after Phil Edwards had tangled with Chris Beardsley.
The visiting goalkeeper continued to defy home pressure until nine minutes after the break when he brought down Beardsley in his area. He somehow escaped a red card and dived full length to push Alan Sheehan's spot-kick away.
He was finally beaten by Hamshaw's 58th-minute free-kick to set up the thrilling finale in which both sides found the target.
Even at 2-2, Accrington had a chance to snatch all three points, but Edwards hit the post when well placed.