The 1-18 to 1-17 loss to the defending champions means that Michael Ryan's side now face a major task to qualify for the knock-out stages of the competition.
Tipp suffered a blow before the throw-in when the returning Seamus Callanan had to withdraw from the game owing to a hamstring injury.
However, the Premier County made a good start to the clash with the Deise and had built up a 0-14 to 0-9 lead by early in the second period.
After that, though, things began to turn in favour of the visitors – Waterford scored 1-4 without reply (their goal came from Tom Devine) and seemed set for the win.
Tipp weren't done yet and a goal from John McGrath (who also notched two points), following good work by substitute Jack Bergin, put them back in front with time fast running out.
Waterford drew level again shortly afterwards courtesy of a Patrick Curran point paving the way for Gleeson to get the winner.
Tipperary's other scorers were John O'Dwyer 0-9, Michael Breen 0-2 and Brendan Maher and Noel McGrath with 0-1 a piece.
The Premier County face Galway next Sunday at Pearse Stadium in what is shaping up to be a make-or-break fixture.
