Dale match Red
Before the break, Jimmy Keohane lofted a great ball into the box and Harrison Hopper, who slid in to get on the end of it, turned it agonisingly over the bar.
Luca Ercolani fired a low effort just past the far post, before Ethan Brierley drew the last save of the half.
The young Dale midfielder struck goal wards from 25-yards, forcing Mastny to tip the dangerous shot round the upright.
Six minutes after the restart, Rochdale were awarded a penalty after Hopper was upended in the area.
Morley took the resulting spot-kick but was superbly kept out by the United goalkeeper, who saved low to his right. He was also kept out on the rebound.
Keohane sent an effort wide shortly before a double change took place on the hour mark, when Ollie Rathbone and Alex Newby replaced Lund and Beesley, respectfully.
Substitute Rathbone very nearly broke the deadlock soon after his introduction but he was denied by the woodwork. Keohane had a low shot saved and he struck the post with the follow up.
Dale’s third final substitution came in the 82nd, as Academy scholar Kacper Mialkowski replaced Brierley to make his debut.
Sixty seconds after the change, Dale hit the visitors on the counter-attack and Newby struck inches wide.
Neither side could find a breakthrough, and with the game level at fulltime, it went straight to penalties for a bonus point.
Morley failed again from 12 yards in the shootout with United a goal up through Hannibal Mejbri and Charlie McCann gave them clear daylight.
Alex Newby converted for Dale before Charlie
Wellens was foiled and Tavares stepped up to emphatically level.
United pulled ahead 4-3 to herald sudden death and Rathbone prolonged the contest, via Mastny’s palms.
Hugill converted for United before Mastny pulled off a superb save to keep out Hopper’s spot kick and send the visitors home with a bonus point.