As the club celebrated Dockers Day in the presence of Millwall's mid-1960's side, who once went on a 59-game home unbeaten run, Martin was inspirational in having a hand in all his side's goals.
Millwall began brightly with Ali Fuseini and Laird impressive in midfield as Vale's hapless backline, having shipped 14 goals in their last six outings, looked shaky every time the hosts attacked.
After wasting several promising opportunities the Lions took the lead after 18 minutes. Winger Martin squeezed an intricate ball between two Vale defenders to Gary Alexander. His lay-off found Grabban who slotted home from the edge of the box.
Millwall failed to double their advantage soon after with Grabban firing at keeper Joe Anyon.
Bottom-placed Vale temporarily managed to restrict Millwall's momentum and striker Danny Glover and centre-half Keith Lowe may both have done better on two rare forays forward.
Alexander should have put his side two up but fired at the feet of Anyon with the goal at his mercy. However, with one minute of the half remaining, Millwall extended their lead.
A whipped cross by Martin was met at the near post by Laird who flicked home on the volley.
Millwall continued to pin Vale back in the second half, with the lively Martin and Jay Simpson terrorising the visitors' full-backs.
A rampaging Grabban should have made the game safe, but fired wide while Kyle Perry, still awaiting his first league goal for Vale, headed wide from ten yards.
The moment of the game came in the 68th minute, a slaloming Martin travelling 40 yards before firing home, capping a wonderful individual display and sealing all three points for his side.