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 Lancashire side.
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 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.
It looked as if the Robins would claim another morale-boosting win until the fifth minute of stoppage time when a cross from Daniel 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.
Oldham remain eighth in the table, five points behind Scunthorpe United in the final play-off position.
MK Dons let a two-goal lead against Crewe Alexandra slip away, apparently along with their chances of automatic promotion.
They had cantered in to a 2-0 lead with goals from Aaron Wilbraham and Jason Puncheon. They had further chances to extend their lead as Crewe never looked like scoring, until the 78th minute, when Mark Carrington headed home superbly.
Then Willy Gueret brought down Alan Sheehan minutes later with Gylfi Sigurdsson sending the keeper the wrong way from the spot.
Carlisle United's relegation fears moved a step closer to becoming a reality when relegation rivals Hereford United recorded a 2-1 win at Brunton Park.
Steve Guinan and Ben Smith had put the Bulls into a 2-0 lead, and although Michael Bridges pulled one back the Cumbrians lacked a killer instict.
Simon Cox returned to Sixfields to complete a hat-trick as Swindon Town leapfrogged Northampton Town in the fight to stay out of the relegation zone after a 4-3 win.
The lively Swindon striker thanked his former teammates with a super treble while striker partner Billy Paynter also got on the scoresheet in a seven-goal thriller.