Goals from Matt Hewlett, Brian Howard and topscorer Sam Parkin earned Swindon their second win in three days.
Brentford, who are lingering on the edge of a play-off place, forced eight corners throughout the game but failed to muster a single shot on target as they slipped to their second defeat over the Christmas period.
But it was the visitors who almost took an instant lead in the third minute when Jay Tabb's in-swinging corner was met at the near post by defender Sam Sodje only for his close-range header to sail just wide of the post.
On-loan midfielder Lee Holmes flashed a shot wide for the home side on six minutes and David Duke should have done better on 25 minutes when he dragged a shot wide when played in by Igoe.
But Brentford's dominance eventually paid off three minutes before the break when a poor Sodje clearance fell to Hewlett 25 yards out and he curled an effort past keeper Stuart Nelson to give the home side the lead.
Swindon defender Luke Garrard had to be alert just after the interval to clear Steve Claridge's dangerous centre before a pinpoint Igoe cross on 66 minutes led to Swindon doubling their advantage.
Following Duke's throw in Igoe found Howard at the far post and his looping header nestled into the bottom corner over the head of Nelson.
Ten minutes later Swindon added a third but this time a Steve Jenkins cross found top scorer Parkin six yards out but he held off the challenge of defender Jamie Lawrence to head in his 10th goal of the season.
Eight minutes from time ex-Swindon loan man Deon Burton almost grabbed a consolation for Brentford but blazed his shot from 10 yards high over the bar to sum up their day.