Reading loan-man Hal Robson-Kanu got the first goal for Swindon, who moved above Yeovil Town and out of the bottom four.
Swindon rode their luck early on and could have been chasing the game before Robson-Kanu fired them into a 13th-minute lead.
Adam Barrett sent a header straight into goalkeeper Phil Smith's hands and Theo Robinson had an angled shot beaten out before the keeper saved from Lee Barnard.
It was from Phil Smith's save that Swindon stole the lead - Anthony McNamee climaxing a quick break by feeding Robson-Kanu to score.
Six minutes later Swindon, who had not won any of their previous six matches, struck again. Osei Sankofa was yellow carded for a tackle from behind on Billy Paynter who, under pressure, was trying to tee up a shot.
There were few protests as Bolton Wanderers target Cox drilled his 21st goal of the season into Steve Mildenhall's bottom right-hand corner.
The early nervousness Swindon had shown evaporated, while Southend became distinctly average and seldom posed much threat on the Wiltshire goal.
With 18 minutes left, manager Steve Tilson made a triple substitution in a vain attempt to inject some life into his stagnant side.
It had little effect, save Swindon breaking away to score a third, two minutes from the end of normal time, after a controversial penalty award.
Michael Timlin appeared to fall spectacularly when Robinson made a challenge, but Greater Manchester referee Keith Evans pointed to the spot.
Cox gleefully rammed his 22nd strike of the season into the roof of the Southend net. The result, which boosted Swindon's survival prospects, probably ended any faint hopes Southend had of making the play-offs.