Francis cut in from the right to see his 20-yard shot deflect off Swindon defender Hasney Aljofree and loop over the goalkeeper into the net via the crossbar.
This was just reward for the visitors who had dominated in the early exchanges, but they then seemed content to sit on their lead.
Swindon came back into the game, but there was little quality from either side although Mark Gower did produce some good work on the visitors' left.
Jon-Paul McGovern and Barry Corr had both earlier gone close for Swindon, but there was little to cheer for the home fans.
Swindon's woe continued just before the interval when Corr's injury-plagued season continued with what appeared at the time to be a shoulder injury.
Later Town manager Maurice Malpas confirmed that it was a shoulder injury which is likely to rule him out for the rest of the season and possibly longer.
Lee Peacock substituted for Michael Timlin at the start of the second half, but this tactical change made little difference as the visitors continued to have the better of the game.
Alan McCormack might easily have wrapped the game up with a second goal early in the second half, but was marginally offside as Gower's excellently judged cross reached the striker inside the home penalty area.
Swindon increasingly looked a ragged outfit as the visitors bossed the midfield, but could not find a decent finish.
Three scares in the closing moments might have seen former Southend player Billy Paynter equalise, but a brilliant save by Darryl Flahavan on one occasion and a wasteful shot over the bar on another, meant Southend kept their play-off hopes on track.