Scott Cuthbert scored his first goal for Swindon on 21 minutes after being left unmarked 10 yards out following a McGovern free kick to make it 1-0.
Southend were then reduced to 10 ten after Christophe dropped to the floor with a clear dive, then after the play carried on it made a quick recovery, so was shown a second yellow card and sent off.
Sub Temitope Obadeyi then scored for Swindon with a shot which went through Steve Mildenhall's legs and into the back of the net to make it 2-0 on 79 minutes.
Southend pulled a goal back a minute later with a shot from Scannell from just inside the box making it 2-1.
Swindon hang on to take all 3 points, which moves them up to 8th place in the table.