Kyle Joseph gave the Robins a 14th-minute lead and it looked like the lead would stand up until Hiram Boateng equalized three minutes from time.
The Dons are tenth on nine points following this result while the hosts find themselves in 16th with six points.
Story of the match
The hosts went close just four minutes into the match as William Boyle got on the end of some service from Sean Long, but his header from the centre of the box was just wide.
After Alfie May saw a shot blocked and Matty Blair and Liam Sercombe were off-target with their attempts, Cheltenham opened the scoring after 14 minutes.
Long was the provider as he fed Joseph, who beat Andy Fisher with a left-footed shot into the bottom right corner to give the Robins the lead.
Fisher then had to make a smart save as he denied Chris Hussey and at the other end, Charlie Brown had a pair of chances blocked and a third opportunity by Harry Darling was again turned away by the Cheltenham defense.
In first-half stoppage time, Hussey fed Boyle, but Fisher was alert to the danger to cap off a cagey first half that had the hosts ahead. On 54 minutes, Daniel Harvie had a chance for the Dons, but shot high.
Six minutes later, Hiram Boateng had a golden opportunity to level for the visitors, but his shot from the center of the box was stopped by Scott Flinders.
From a set piece, Lewis Freestone headed for Taylor Perry, but his shot from the right was just off the mark. Finally, the Dons evened the score as Boateng beat Flinders to make it 1-1.
Hussey then missed from 40 yards out on the left wing in second-half stoppage time and that was the last chance of the match as the spoils were shared.
Man of the match: Hiram Boateng
In a mostly defensive match with few clear-cut chances, Boateng took his to help his side to a point after seeing his 58th-minute opportunity denied by Flinders.