Tresor Kandol's last-minute winner gave Leeds victory as Dennis Wise's side began their first season in League One.
Leeds, who started the campaign with a 15-point deduction, fell behind when Chris Greenacre arrived at the back post to convert a Chris Shuker cross.
But the visitors fought back after the break and levelled when Matt Heath headed home Alan Thompson's free-kick.
Kandol snatched all three points when he bundled home and Andy Hughes cross in the dying seconds of the game.
Tranmere: Coyne, Stockdale, Chorley, Goodison, Sherriff,
McLaren, Jennings, Shuker (Curran 83), Zola,
Greenacre (Taylor 80), Davies.
Subs Not Used: Achterberg, Tremarco, Kay.
Booked: Stockdale, Chorley, Goodison.
Goal: Greenacre 22.
Leeds: Ankergren, Richardson, Marques, Heath, Lewis,
Weston (Flo 76), Thompson, Westlake, Hughes,
Beckford (Howson 90), Kandol.
Subs Not Used: Carole, Parker, Elliott.
Booked: Beckford, Kandol, Thompson, Westlake.
Goals: Heath 55, Kandol 89.
Ref: L Mason (Lancashire).