Man United started well, with Marcus Rashford drawing a smart save from Villa goalkeeper Emiliano Martinez, while Morgan Rogers and Jaden Philogene had decent attempts for the hosts inside the first 20 minutes.
It was much better from the Red Devils in possession of the ball, but there were still concerns through the middle, with Villa having a number of opportunities to break through in the opening half of action.
Martinez also had to keep out a strike from Alejandro Garnacho in the latter stages of the first period, but the score was level at the end of a first 45 minutes which lacked quality from both sides.
Man United goalkeeper Andre Onana made an excellent stop to keep out a Youri Tielemans strike early in the second half, and the two teams were still level heading into the final 30 minutes of action.
Bruno Fernandes rattled the crossbar with a free kick for Man United, while Villa had a couple of late chances, including through Philogene, who had a goal-bound shot blocked by Diogo Dalot, but neither side did enough to deserve all three points on Sunday afternoon.
The result has left Villa in fifth spot in the Premier League table, boasting 14 points from seven matches, while Man United stay in 14th spot in the division, claiming eight points from their first seven games.
ASTON VILLA VS. MAN UNITED HIGHLIGHTS
Bruno Fernandes free kick vs. Aston Villa
Man United come close to making the breakthrough at Villa Park, as Fernandes sends a free kick towards the top corner, but the crossbar comes to the home side's rescue.
MAN OF THE MATCH - JONNY EVANS
Evans will be 37 in January, but he is still a top-class performer when his body allows him, and he was the best player on the pitch at Villa Park, performing a leading role in Man United securing a point.
The defender won two aerial duels and made four tackles, while he finished with a pass success rate of 87%, and it is a real shame for Man United that he is not able to play every single match.
ASTON VILLA VS. MAN UNITED MATCH STATS
Possession: Aston Villa 54%-46% Man United
Shots: Aston Villa 10-9 Man United
Shots on target: Aston Villa 1-4 Man United
Corners: Aston Villa 6-3 Man United
Fouls: Aston Villa 13-11 Man United
WHAT NEXT?
Man United will return to action after the international break at home to Brentford, with the Bees visiting Old Trafford on October 19. Villa, meanwhile, will be in action on the same afternoon against Fulham.
It remains to be seen whether the draw and performance is enough for Erik ten Hag to keep his managerial job at Man United beyond the October international break.