Danny Wilson hailed his side's fantastic performance, but refused to get carried away after only their second win in the last five outings.
Swindon inflicted a 1-0 defeat on fellow promotion hopefuls Southampton, with Charlie Austin's goal making the difference between the sides.
"To a man, every single man in a Swindon Town shirt gave 100% and I'm delighted with my players," a delighted Wilson said.
"We have come through a bit of a sticky patch and we are right in there [for promotion], but we are still so far away from where we want to be at the end of the season."
He added: "We need to keep believing in ourselves because we are more than capable of results like this."
Yeovil manager Terry Skiverton was quick to praise the match-winning skill of Adam Clayton following his side's 1-0 defeat at Carlisle.
The on-loan Manchester City youngster sent a half-volley dipping over Alex McCarthy after the Yeovil goalkeeper had punched out Marc Bridge-Wilkinson's second-half corner.
Skiverton said: "We defended very well, but sometimes you have to look at moments of quality and stand back and applaud them. Clayton has that quality. He gets the ball and sprays it around and for us we knew he would be a danger man."
Strugglers Oldham battled through a dismal game to claim a 1-0 victory over relegation-haunted Stockport at Edgley Park.
Pawel Abbott's 24th-minute penalty eased the pressure on Oldham boss Dave Penney still further after a fourth game without defeat.
He said: "It's good to get the three points - this is a big win for us undoubtedly. We knew it would be tough, their pitch has been well documented and it is difficult. It's been nice to finally play the game though after a couple of postponements earlier in the season."
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