Emmanuel Dennis put Steve Cooper's side ahead early in the first-half at the City Ground before Young bagged Villa's equaliser with a long-range rocket.
By ending their five-match losing run, Forest moved one point above Leicester City into 19th place.
But Forest have won just once in their nine league matches this season and face a huge battle to avoid relegation back to the Championship.
Villa are unbeaten in their last four games, but Steven Gerrard's team are also in relegation danger; they've won only once in their last seven league matches and sit just three points above the bottom three.
Forest took the lead with a well-worked free-kick as Morgan Gibbs-White's delivery picked out Dennis for a glancing header past Emiliano Martinez from six yards.
It was Dennis' first Forest goal since joining from Watford for £20m in August, but Villa produced the perfect response seven minutes later.
Ollie Watkins nodded down to Young 25 yards from goal and the left-back's lashed a strike into the bottom corner.
Forest appealed for a foul by Villa's Jacob Ramsey on Ryan Yates in the build-up, but Young's first goal for the club since 2011 was allowed to stand.
At 37, Young is Villa's second-oldest scorer in the Premier League behind Peter Schmeichel, the Danish 'keeper who was just a few months older when he netted in 2001.
Villa had failed to win all four times they had conceded first this season, but they pushed hard to end that streak.
Watkins had the ball in the net from Philippe Coutinho's cross moments later, but Villa were denied by an offside flag.
Watkins also forced Forest's Dean Henderson to save his header at the near post, before Cheikhou Kouyate's long-range blast drew a good stop from Martinez at the other end.
Cameron Archer had a chance to win the game for Villa in the final minutes, but his header from Luiz's free-kick was well off target.
