After a couple of earlier chances Swindon took the lead on 33 minutes after a cross from Onibuje found Monkhouse, who passed to Pook who then scored from close range to give Swindon a 1-0 lead.
On 44 minutes Swindon made it 2-0 with a 20 yard shot from Andy Monkhouse finding the back of the net.
Grimsby didn't really look like scoring, although Peter Brezovan did have to make a couple of good saves. Then on 75 minutes he fell badly after making another save landing on his arm. He was stretchered off, and with no keeper on the bench Adi Williams had to go in goal for the final 15 minutes.
Williams was called into action a couple of times when he had to catch the ball, and he also had to make a diving save, but much of the time the Swindon defence kept the ball away from him.
Lee Peacock then made it 3-0 to Swindon on 88 minutes after he was able to lob the ball over the advancing Grimsby 'keeper.
Overall a good win, but he was overshadowed by Brezovan's suspected broken arm, The win moves Swindon back up a place into 3rd. Swindon now take a break from the league and go back to Wycombe on tuesday evening this time in the Johnstone's Paint Trophy. 3 weeks ago Swindon picked up a 1-1 draw against Wycombe when Tommy Mooney scored a last minute equaliser for them.