St Mirren’s lead at the top of the Championship was reduced to three points as Morton responded to an opener from Celtic-bound Lewis Morgan to draw.
Just as Morton started to work their way into the game after early Buddies pressure, the 21-year-old winger pounced to fire home from 12 yards.
Mullen was denied by the inside of the post as St Mirren looked to extend their lead.
But Thomas O’Ware rose to head the equaliser with 10 minutes remaining.
With the Premiership having gone into a three-week winter hibernation, St Mirren prospect Morgan was the centre of attention as he nears a transfer to Celtic that appears likely to see him loaned back until the end of the season.
The winger has said he wants to help the Buddies win the title and promotion before leaving for the Scottish champions and they made the trip to Greenock seeking a fifth straight victory – and a fifth away from home – after having beaten nearest challengers Dundee United on Saturday.
But they had lost 4-1 in their last visit to Cappielow in August, were also held to a 2-2 draw by Morton in Paisley in October and another derby without a win allows United to narrow the gap once again after their convincing win over bottom side Brechin City.
Morton had also only lost once in their last five outings, but Jack Ross’ visitors had them pinned back in the early stages.
The ball failed to fall kindly as crosses were peppered around the home penalty box – until Ian McShane curled a fine cross into the path of Danny Mullen in front of goal.
Although Michael Doyle won his wrestling match with the St Mirren striker, it was deflected into the path of Morgan to finish low and clinically into the far corner.
A Mullen shot came off the post before being gathered by goalkeeper Derek Gaston as St Mirren threatened to extend their lead.
However, the visitors were lucky to escape a penalty claim when Robert Thomson appeared unfortunate to be booked for simulation after being clipped by Jack Baird.
Michael Tidser lashed a drive over from a promising position and another Morton penalty claim was waved away by referee Kevin Clancy when a Gary Oliver shot struck Baird.
An encouraged Morton flew at their visitors after the break and Jai Quitongo forced a near-post save from goalkeeper Craig Samson.
Despite the home pressure, heightened tensions and tempers on edge, St Mirren supplied a moment of humour as Cypriot left-back Stelios Demetriou ate a chocolate bar thrown at him from the stands before completing his throw-in.
However, the game turned sour for the Buddies as the equaliser finally came when O’Ware escaped his marker to head in a Jonathan Tiffoney corner.
Substitute John Sutton screwed a header across the face of goal as St Mirren pressed for a late winner, but Morton held on to remain in fifth spot ahead of Queen of the South on goal difference.
Greenock Morton defender Thomas O’Ware: “In the second half, we were more like ourselves. In the first half, it showed we had not had a game in a week and we were rusty.
“But we got in at half-time, there were a few words said and the second-half was exactly what we are about.
“We pressed them and didn’t give them any time on the ball.
“We just went for it and obviously we got the goal and were unlucky not to get a second because I think it was a penalty towards the end.”