Striker Sam Parkin fired home his 15th goal this season to help Swindon claim a valuable win to dent Brentford's promotion hopes.
Captain Andy Gurney had given the home side the perfect start after he sent them in front in only the second minute, reacting quickly to lash home defender Matt Heywood's goal bound header.
Better was to follow as Parkin made the most of Brentford midfielder Jamie Fullarton's 51st minute dismissal to double the RobinsÂ’ lead.
Fullarton was sent off for a two footed lunge at on-loan striker Luke Nightingale and Parkin then had no trouble in converting Stefani Miglioranzi's 66th minute corner from close range.
Bees striker Rowan Vine ensured some nervous moments for the home crowd when he reduced the deficit with an unstoppable shot in the 75th minute although Parkin and Danny Invincibile should have restored Swindon's advantage in the closing stages.
Brentford manager Wally Downes was indebted to young goalkeeper Alan Julian for keeping his side in the game in the opening 45 minutes.
Julian was making his league debut because first choice Paul Smith was ill, but he responded with a string of outstanding saves that belied his 18 years.
The teenage goalkeeper dived at full length in the 25th minute to parry Parkin's shot for a corner and then did even better 13 minutes later to block a fiercely struck free kick from Gurney that was heading in to the top left hand corner.
Swindon goalkeeper Bart Griemink was largely untroubled throughout the 90 minutes but showed great reactions to block Michael Dobson's point blank header two minutes in to the second half.