Stanley, faced with the drop just one season after last year's memorable promotion, were just too good for their visitors.
And thanks to goals from Paul Mullin, Sean Doherty, Peter Cavanagh and a penalty from Andy Todd, deservedly took the points.
But it was the sending-off of Gary Croft, just two minutes before the break, which swung the match in the home side's favour, the defender sent off for a deliberate handball.
Grimsby levelled matters four minutes before half-time when Tom Newey coolly slotted past Stanley keeper David Martin, Mullin having broken the deadlock nine minutes earlier.
However, it proved a sorry afternoon for Mariners keeper Phil Barnes.
Todd didn't waste the resulting penalty from Croft's handball, before Cavanagh's free-kick was met by Doherty to set up a two-goal cushion ten minutes into the second period.
Cavanagh got in the act with two minutes to go, completing a superb victory with an excellent finish.
The home side had taken the lead just past the half-hour mark when Mullin caught the Grimsby defence on the back foot and fired past Phillips with an accurate finish.