Bottom-of-the-table Cheltenham are now unbeaten in their last four games while Oldham have not won in five. Crucially, however, this draw ended a run of three straight defeats for the Latics.
It was certainly not a vintage performance by Joe Royle's side, who played in fits and starts and looked jaded up front against a Cheltenham side already gearing up for next season.
Cheltenham certainly had the best of the first half with yet another re-jigged team - containing the 44th player to be used by the club this season - finding the energy and freedom to pass the ball remarkably well.
Midfielder Andy Gallinagh went close with a shot from the edge of the area and Elvis Hammond, who was a threat to the Oldham defence throughout his time on the pitch, broke clear midway through the first half but goalkeeper Shane Supple made a sharp block with his legs.
Cheltenham had been threatening a goal and they claimed it just after the half-hour mark from a well-worked move.
Youngster Morley Watkins fed debut-boy Frankie Artus - a loan signing from Bristol City - and he exchanged passed with Gallinagh before bursting through the Oldham defence to beat Supple with a low finish.
Oldham's only real chance of the first half came shortly before the break when left-back Daniel Jones sent a free-kick just over the crossbar.
Oldham had more of the game in the second half but they remained frustrated by a young and hard-working Cheltenham team who restricted them to only a handful of chances.
The best of those came from crosses by the useful Jones, who is on loan from Wolves, with substitutes Fabio Ferreira and Lewis Alessandra both heading wide.
It looked for all the world as if Cheltenham would claim another morale-boosting win until the fifth minute of stoppage time when another cross from Jones was headed out to the edge of the area.
Midfielder Mark Allott controlled it and played the ball forward to Whittaker, who smashed in a shot from close range for his sixth league goal of the season.