Gary Kelly's corner in the second minute of added time was directed by May beyond debutant goalkeeper Colin Doyle at the near post.
Leeds hit the post twice in the first half and Doyle also denied Jonathon Douglas with a superb save.
Millwall went closest when Barry Hayles vicious shot from inside the penalty area was tipped over by Neil Sullivan.
Leeds manager Kevin Blackwell on David Healy's last-minute deflected winner:
Blackwell said: "We shaded the game and had the better chances. We hit the woodwork twice, but I didn't think the goal was going to come.
"But we got a fortuitous deflection and we will take that away from home.
"David (Healy) said if it hadn't taken a deflection it was going in the top corner anyway and I believe him."
Millwall: Doyle, Paul Robinson, Williams, Whitbread, Ifil, Dunne, Elliott, Asaba, Craig, Dyer (May 76), Hayles.
Subs Not Used: Vincent, Fangueiro, Cogan, Braniff.
Booked: Hayles, Whitbread.
Leeds: Sullivan, Kelly, Kilgallon, Gregan, Harding, Blake (Moore 92), Miller, Derry (Douglas 37), Lewis, Healy, Hulse.
Subs Not Used: Bennett, Richardson, Walton.
Booked: Gregan, Douglas, Miller, Moore.
Goals: May 90 og.
Referee: M Fletcher (Worcestershire).