The Bees had lost their opening two matches of the season at Bury and Swansea without even scoring, while the Mariners had yet to concede this season.
But a first-half brace from debutant Charlie MacDonald and goals from Nathan Elder and Glenn Poole saw off any hopes of these records continuing.
Grimsby had made all the early running and should have taken an early lead but Martin Butler headed over a Simon Heslop free-kick when well-placed to score.
The Mariners let the home side off the hook again after 14 minutes when Andy Taylor found himself clean through on Ben Hamer's goal after latching onto a punt from defence, but the Grimsby frontman lifted the ball over the stranded keeper and into the relieved home supporters in the New Road stand.
The Bees were finally stung into action and, when they scored against the run of play after 27 minutes, it heralded the beginning of a landslide victory that would do any political party proud.
On-loan Bristol City defender James Wilson was the provider, bamboozling the Grimsby defence with an uncharacteristic jinking run into the box, before rolling a peach of a pass into the path of debutant MacDonald, who gleefully rammed home from 15 yards.
After 35 minutes Nathan Elder put Brentford 2-0 up after a gift from Mariners keeper Phil Barnes.
Brett Johnson floated a hopeful ball into the area which Barnes misguidedly attempted to collect, but Marvin Williams headed across goal, leaving Elder to slot into an empty net.
MacDonald grabbed his second just before half-time, taking advantage of sloppy defending to prod the ball past Barnes from close range.
Grimsby rallied in the second half, but could not get a clean strike at the Brentford goal.
Poole then wrapped up the points on the hour. Elder's clever play in the right-hand channel allowed himself to pick out his team-mate and Poole slammed the ball past the punch-drunk Barnes from 12 yards.