Mark Gower fired the hosts ahead in the first half from Lee Bradbury's cross.
Fredy Eastwood came close to making it 2-0 with a deflected shot before Healy came on with eight minutes to go and rifled home Robbie Elliott's free-kick.
The game ended in chaos when Leeds claimed they should have had a penalty for a Simon Francis handball and boss Dennis Wise was sent down the tunnel.
Leeds manager Dennis Wise:
"You only need to look at the reaction of the Southend players, they all had their hands on their heads.
"I've had problems with him before. I told him I don't want him to referee for me again."
Southend: Flahavan, Francis, Sodje, Clarke, Hunt, Campbell-Ryce (Harrold 83), Maher, Gower, Foran, Bradbury, Eastwood (Sam 83).
Subs Not Used: Collis, Hammell, Moussa.
Booked: Bradbury.
Goals: Gower 24.
Leeds: Ankergren, Richardson, Heath, Michalik, Robbie Elliott, Blake (Healy 82), Kishishev, Douglas, Lewis (Moore 64), Cresswell, Kandol.
Subs Not Used: Stack, Crainey, Carole.
Booked: Robbie Elliott, Kandol, Michalik.
Goals: Healy 88.
Att: 11,274.
Ref: N Miller (Co Durham).