The striker netted just before the hour to get Jim Bentley’s side on level terms after they had deservedly trailed at half-time.
Padraig Amond had given the visitors a first-half advantage but Mullin was in the right place at the right time to earn a point.
Bentley had rung the changes following the Shrimps’ defeat at Cheltenham Town seven days earlier.
Barry Roche (wrist) and Alex Kenyon (suspended) were already unavailable but Dean Winnard, Lee Molyneux and Aaron Wildig were dropped to the bench.
In came keeper Danijel Nizic for his first league start of the season along with Michael Duckworth, Andy Fleming, Rhys Turner and Antony Evans.
Nizic was comfortably the busier of the two keepers in a depressingly one-sided opening half from the home perspective.
Hartlepool were comfortably the more accomplished in possession and enjoyed much the greater attacking threat.
Inside the opening 10 minutes, Nizic had to block Amond’s route to goal and saw Nicky Featherstone shoot well over.
Nathan Thomas’ looping effort was comfortably held by Nizic, Scott Harrison volleyed narrowly wide before Amond came closest of all with a header into the side netting.
Still the visitors pressed for an opener with Rhys Oates heading over from Thomas’ corner before seeing a first-time effort held by Nizic.
Consequently, it came as little surprise when Amond broke the deadlock, finishing smartly from Lewis Alessandra’s pass.
In contrast, Morecambe’s first-half attacking play bordered on the insipid with little in the way of danger for the visitors.
Their direct approach left Mullin feeding off scraps and, when they did get into decent positions, the final ball was lacking.
The closest they came before the break was when Mullin created the opportunity for himself but a saw a shot kept out by keeper Joe Fryer.
The Shrimps came out with noticeably more tempo in the second half but could have fallen further behind on 56 minutes had Edwards not blocked Amond’s shot.
His efforts were rewarded three minutes later when Mullin got the Shrimps on level terms, netting from close range after Edwards’ shot was cleared off the line.
Both sides pressed for a winner with opportunities coming at either end.
Amond and Alessandra were off target within a minute of each other, while Kevin Ellison had one effort saved and sent another off target when stretching to meet Edwards’ flick.
Penalty appeals for handball were waved away, while Bentley brought on Molyneux and Wildig with both going close.
Molyneux had a shot straight at the keeper and Wildig’s goalbound volley struck a defender.
There was still time for Amond to send a free-kick into the wall and for Ellison to head wide at the other end but a point was just about the right outcome - and one Morecambe would have settled for at half-time.
Morecambe: Nizic, Duckworth, Edwards, Whitmore, McGowan, Fleming, Rose, Turner (Wildig 66), Evans (Molyneux 66), Ellison, Mullin. Subs not used: Maher, Wakefield, Winnard, Murphy, Jordan.
Hartlepool United: Fryer, Richardson, Walker, Harrison, Donnelly, Featherstone, Alessandra (Rodney 81), Woods, Thomas, Oates (Deverdics 90), Amond. Subs not used: Dudzinski, Magnay, Bates, Hawkins, Rooney.
Referee: Andy Haines.