Molyneux scored for the second successive game seven minutes from time when he converted a superb ball from Kevin Ellison as the Shrimps maintained their excellent run of form.
It is now just one defeat in 11 games for Jim Bentley’s side who had to come from a goal behind after Kal Naismith had fired the home side into a 64th-minute lead.
Substitute Naismith scored with virtually his first touch when he received the ball and ran on goal before firing a low left-foot shot past Barry Roche from the edge of the area to break the deadlock.
Portsmouth went close to a second moments later when Conor Chaplin drilled a low shot just wide from the edge of the box.
Christian Burgess did go close in injury time to giving the home side the three points but he was denied by Roche after a goalmouth scramble.
The first half ended goalless despite plenty of attacking intent from both sides.
The first chance came on four minutes when former Shrimps star Carl Baker forced a good early save from Roche.
On five minutes Preston North End loan man Eoin Doyle looked to have a free run on goal but Alex Whitmore produced a last-ditch tackle just as the striker went to pull the trigger.
The Shrimps hit back and Paul Mullin saw a shot cleared off the line but the effort would have been ruled out for a foul on home keeper David Forde.
Roche remained busy saving a shot from Gareth Evans with his feet before Pompey saw a penalty claim waved away when Enda Stephens went down in the box.
Doyle then missed a golden chance just after the half hour when he headed wide from close range.
But the Shrimps again hit back with their usual counter attack and Aaron Wildig was denied an opener on 31 minutes by a superb save from Forde.
The Shrimps ended the half strongly and created another good chance of the own when Rhys Turner found space in the box but could only head straight at Forde.
Morecambe started the second half strongly with Mullin firing wide when he should have played in Wildig and the same player fired weakly wide.
Portsmouth’s first effort of note after the break came on 62 minutes when Doyle failed to find the target from a Bennett cross before Naismith’s opener.
The Shrimps were not to be denied though as their fine 2017 continued, Bentley’s men ending the evening 14th in League Two and six points off the play-offs.