John Coleman's struggling side last won on opening day in early August when they beat Wycombe 1-0.
But thanks to Mullin's clinical 48th minute header and a 69th minute strike, which came after Paul Bolland had cancelled out Proctor's spot-kick, the home side deservedly took the points.
And to rub salt into an already gaping wound, Proctor found the back of the net in injury-time to complete a comprehensive win.
Accrington were desperate for a victory having been on the receiving end of five consecutive defeats, while Grimsby were looking for a second successive win having hammered Huddersfield 4-1 in midweek.
However, the visitors gifted their opponents their opener. Defender Tom Newey needlessly felled Proctor in the box and he duly stepped up to coolly slot the ball past keeper Phil Barnes.
Mullin doubled the home team's advantage three minutes after the resumption with a pinpoint header, before Bolland pulled a goal back in the 57th minute when his powerful header was too good for Accrington keeper Kenny Arthur.
But when Mullin scored his second, the damage had been done and Proctor completed the rout with a fine finish at the death.
Grimsby started the better and went close through Ciaran Toner in the seventh minute, but his shot was blocked.
Roscoe D'Sane fired over for Accrington and Peter Cavanagh had a fierce shot saved in the first half.
Bolland went close for Grimsby and Isaiah Rankin had a shot blocked as they chased the game after Proctor's and Mullin's early goals.
But not matter how hard they pressed, and despite Bolland's excellent header, it was Proctor and Mullin who scored again to make sure of the points.