Despite having nothing but a potential league phase top spot to play for, Villa went straight on the offensive, with Ollie Watkins and Harvey Elliott forcing Alexander Schlager into a double save inside 30 seconds.
The hosts continued to look mostly comfortable, but they had Emiliano Martínez to thank for keeping things level when Soumaila Diabate fired a shot from the edge of the area, before Karim Konaté was also thwarted on the rebound.
The tempo slowed after that, something which suited Salzburg as they pressed eagerly, forcing Villa into a mistake for the opener.
Tyrone Mings hesitated in passing to his goalkeeper, allowing Edmund Baidoo to steal the ball at the byline and square it to Konaté, who shuffled it into the open goal despite Victor Lindelöf’s efforts.
Salzburg remained on top until HT, and went into it fully warranting their lead and perhaps deserving of more after Baidoo tested Martínez late on.
But they didn’t have to wait too long in the second half to make it two, as Kerim Alajbegović ventured past a couple of challenges in the area and fizzed a low ball to the near post, where substitute Moussa Yeo found the net with a brilliant backheel flick.
But the tide soon began to turn, and Villa halved the deficit when Emiliano Buendía and Morgan Rogers combined in a silky passing move, culminating in Rogers slotting inside the near post.
No Premier League side had won more points from losing positions so far this season, and Villa took that form onto the European stage with two more goals late on to complete a sensational comeback.
Matty Cash’s teasing inswinger was met ahead of Schlager by Mings, who made up for his earlier mistake in nodding into the net.
Then, with a few minutes remaining, a pair of young substitutes combined, with Kadan Young working his way into the area and sliding it across for Jamaldeen Jimoh-Aloba, who expertly side-footed past the goalkeeper on his first European appearance.
Salzburg’s performance until Villa’s first goal was spectacular, but it may have been some consolation that even a victory wouldn’t have sufficed to send them to the play-offs.
Villa, meanwhile, keep their 10-match unbeaten home record in Europe going, and finish the UEL league phase in second place with seven wins from eight matches.
Flashscore Man of the Match: Morgan Rogers (Aston Villa)