Goals either end of the match from Adam Barrett and substitute Wayne Gray were enough to earn Southend their third successive league victory.
Southend's win propelled them up to sixth in the table and left Swindon precariously close to the bottom.
The quickfire visitors took just 70 seconds to take the lead, when defender Barrett headed in Kevin Maher's precise free-kick.
And they were close to doubling their lead just four minutes later through another Maher free-kick which keeper Tom Heaton superbly turned around the post.
Swindon should have levelled on ten minutes when Michael Pook's right wing cross found Andy Gurney three yards pout, only for the defender's header to somehow go over the bar.
Swindon's unknown keeper, Heaton, was called in to action in 18 minutes when he dived acrobatically to his let to keep out Luke Guttridge's 30-yard volley.
But the keeper was left motionless on 27 minutes when Mitchell Cole's left-wing centre found Mark Gower at the back post, only for his header to sail inches wide of the left-hand post.
Veteran striker Shaun Goater showed his class just before the interval when he turned neatly, only to drag his left-foot shot wide.
Swindon made a double substitution at half-time, bringing on Ricky Shakes and Tony Thorpe in place of Gareth Whalley and Jamie Cureton to shore up their attack.
But it was the visitors who again started the half strongly, and Goater was inches away from connecting from Cole's cross midway through the half.
Swindon had a lot of the ball, but found it difficult to break down a stubborn Southend defence, marshalled by man of the match Barrett.
The visitors grabbed a deserved second two minutes from time when another Maher free-kick was this time headed in by sub Gray. But the visitors conceded soon after when Rory Fallon scored a tap-n to set up a tense finish.
Deepinto injury time, almost fashioned an unlikely point when his header from a Thorpe cross sailed agonisingly wide of the post.
