Chris Wdowczyk and Lee Maturine were also on target with an own goal completing the scoring as Town gained quick revenge for their weekend defeat at the hands of the same opposition.
The visitors had the getter of the opening exchanges with Darren
Hanslip, Lewis Buckthorpe, Richard Creer and Nathan Ireland all trying their luck from distance without really troubling Brighouse keeper Paul Brown.
But it was Town who broke the deadlock after 21 minutes when Jermaine Manners and Danny Ryan combined on the left allowing Wdowczyk to crash the ball home from an acute angle.
That gave the home side confidence with David Phelps causing plenty of problems for Grimsby down the right and Ryan tormenting them on the other flank.
And they doubled their advantage five minutes before the break when Phelps set Manners free down the right and his low cross was forced home at the far post by Crossley.
Hanslip, Anthony Rockhill and Buckthorn all had opportunities to pull one back before the break but could not get past Brown.
And Brighouse went on to dominate the second half as they took a grip on proceedings.
Phelps and Manners both went close before Brighouse increased their lead just before the hour mark, Ireland heading a Manners corner into the roof of his own net.
And two minutes later Phelps crossed from the right for Crossley to bag his second with a diving header.
Damian Gomersall had a header cleared off the line as Brighouse looked for more and Manners flashed a shot across the goal and wide moments later.
And they finally got a fifth with 11 minutes remaining when Phelps played the ball through for substitute Maturine and he slid it home.
"I am delighted for the players," said boss Mark Brier, whose side had lost their previous four games.
"We have quality in the changing room and they were all pulling for each other.
"Jermaine Manners has outstanding qualities on and off the pitch and Mark Brady adds another dimension to our game.
"We are not going to get carried away, but it was nice to have had a game that finally reflected a performance.
"We weathered good pressure from Grimsby in the first half and, for once, we were not punished."
The full article contains 415 words and appears in Evening Courier newspaper.