Richie Foran's dramatic injury-time strike lifted Southend out of the Championship relegation zone.
The substitute pounced from 12 yards after Wade Elliott's weak back-header as the Shrimpers climbed to 20th.
Ade Akinbiyi and Steven Caldwell were guilty of missing chances for Burnley in an otherwise turgid first half.
But the hosts improved after the break and Freddy Eastwood twice went close before Foran struck to condemn Burnley to their 17th game without a win.
Southend manager Steve Tilson:
"This was another battling performance full of spirit and character.
"Those were qualities which we needed because Burnley proved tough opponents
and did not let us play as we wanted.
"This is massive for us and sends us into the game against Leeds with a spring in our step. But we must guard against complacency."
Burnley boss Steve Cotterill:
"We did not deserve to lose but in the end paid the penalty for a mistake at the death.
"We are in a terrible rut and things are not going our way. That always seems to be the case at the bottom.
"All we can hope for is that a little bit of luck starts going our way."
Southend: Flahavan, Francis, Sodje, Clarke, Hunt, Campbell-Ryce (Sam 70), McCormack, Maher, Gower (Harrold 80), Bradbury (Foran 70), Eastwood.
Subs Not Used: Collis, Hammell.
Goals: Foran 90.
Burnley: Coyne, Duff, McGreal (Foster 7), Caldwell, McCann, Elliott, James O'Connor, Gudjonsson (Lafferty 60), Harley, Gray, Akinbiyi, Foster (Spicer 74).
Subs Not Used: Jones, Djemba-Djemba.
Booked: Gudjonsson, Harley, James O'Connor.
Ref: P Taylor (Hertfordshire).