Orient enjoyed plenty of possession, but were unable to turn that into a much-needed goal, and after a spell of pressure, Mullin curled an effort into the net to condemn Orient to defeat.
There were two changes from the side which lost 2-1 at home to Carlisle United on Saturday with Victor Adeboyejo making his first league start ahead of Rowan Liburd, while Yvan Erichot came in for the injured Callum Kennedy.
Kennedy’s absence led to reshuffle at the back with skipper Nicky Hunt moving to left back and Erichot slotting into the centre alongside Tom Parkes.
Orient enjoyed the bulk of the possession in the opening stages and created the first opening on four minutes when Gavin Massey’s cross found Nigel Atangana but the Frenchman’s touch was heavy and Barry Roche was able to gather.
The Shrimps first chance came after 11 minutes and it fell to the evergreen Kevin Ellison kindly in the box, however Myles Judd was there to head away the danger.
Orient were showing plenty of encouraging signs throughout the half, but lacked the killer instinct in the final third.
On the half hour mark Ellison put in a delivery from the left and Sargeant did well to hold, before the ball was kicked out of his hands by a Morecambe attacker and referee John Brooks awarded a free-kick.
There was some lovely build-up play for the O’s with Dalby and Collins particularly impressing. One such move resulted in a Massey shot with the outside of his right boot being tipped behind by Roche in the Shrimps goal.
From the resulting set piece the ball fell kindly for Parkes but the centre-half fired wide, much to his and the O’s frustration.
He got another bite at the cherry just before the half was out as he connected with Semedo’s corner, but Roche was equal to the effort before Massey got another teasing ball in across the box, but Adeboyejo failed to connect.
That proved to be the final action of the half, but Orient showed plenty of positive signs and were cheered off at the break.
No changes were made before the second half began, and much like the first period, the second was slow to get going.
It was Orient who did get going and some further good build up play went unrewarded as Massey and Semedo both saw shots saved comfortably by Roche.
Sargeant was forced into his first real save up the other end and it was an excellent one from the youngster as a move involving the front three of Morecambe saw Ellison through on goal.
But out came Sargeant and he got a touch on the effort to deflect it behind for a corner, while up the other end Parkes went close once again as he headed over.
Morecambe launched a quick attack and substitute Rhys Turner almost fired past Sargeant with his first touch, but it went over the bar.
The game was certainly end-to-end and only a fine last-ditch intervention from Judd denied Wildig a certain goal at the near post.
But the O’s could only survive for so long though and with 73 minutes on the clock were dealt a huge blow when Mullin was allowed time to turn and shoot to curl past Sargeant and leave the O’s up against it.
Orient tried to push for the equaliser, but were left high and dry in their hopes as chances were at a premium and O’s were left to contemplate what may have been for the second home game in succession.
Despite not picking up the result the one positive was the return of Liam Kelly following a long injury lay-off as he replaced Michael Collins late on. His presence could well play a big part between now and the end of the season.
ORIENT: Sargeant, Judd, Parkes, Erichot, Hunt, Semedo, Atangana, Collins (Kelly 90), Massey, Dalby (Liburd 77), Adeboyejo (Koroma 90).
SUBS: Grainger, Moore, Mezague, Clark
BOOKED: Semedo (72), Collins (82).
MORECAMBE: Roche, Edwards, Winnard, Mullin (McGowan 82), Murphy, Molyneux (Turner 65), Ellison, Wildig, Whitmore, Duckworth, Rose (Kenyon 75).
SUBS: Nizic, Wakefield, Conlan, Evans.
GOALS: Mullin (72)
BOOKED: Mullin (73), McGowan (83)
REFEREE: John Brooks
Attendance: 2,660 (58 Morecambe fans)