A 1-0 away defeat to AS Monaco saw Villa drop out of the top eight ahead of their final league phase clash with Celtic, but a whirlwind start at Villa Park lifted the home side back into those crucial spots in the live standings.
Inside three minutes, some fluid interplay between Youri Tielemans and Jacob Ramsey released the latter down the left, who picked out Morgan Rogers with a low ball into the box that was expertly tucked home for his first UCL goal.
Less than two minutes later, Rogers doubled that tally when he tried his luck from the edge of the box, beating Kasper Schmeichel with a deflected shot that sailed into the top corner.
The visitors were firmly on the back foot, almost conceding a third when Ramsey hit the post and the ball looped up off Schmeichel’s ankle.
Soon after, a Ramsey-led counter-attack was worked to Ollie Watkins, whose shot was cleared off the line by Alistair Johnston.
To this point, Celtic had rarely threatened, yet a pair of quickfire goals from Adam Idah left the home fans shell-shocked.
Finding himself free down the left, Greg Taylor put in a cross that was diverted by boyhood Celtic fan John McGinn, allowing Idah to turn in with an improvised finish.
Armed with the momentum, the Bhoys drew level before HT thanks to a neat move that culminated with Reo Hatate pulling the ball across for Idah to thrash home.
Perfectly poised after the restart, a point would do little for either side, leading to an absorbing open contest.
On a hat-trick, Rogers stroked a low effort wide of the far post, but he played a crucial role as Villa retook the lead shortly after, holding off a challenge to set his side away on the break.
McGinn was equally important in the build-up as he charged forward before feeding Ramsey, who laid the ball off for Watkins to calmly finish.
Incredibly, the England international could have had another goal moments later when Schmeichel gave the ball away cheaply, but the goalkeeper atoned for his error to deny Watkins superbly.
The chaos continued when referee Clément Turpin pointed to the spot, adjudging Auston Trusty to have unjustly brought down Watkins.
With the opportunity to bag his brace, Watkins couldn’t keep his footing from the spot, sending his penalty ballooning over the bar as he hit the ground.
The Villa forward was again thwarted by the Celtic shot-stopper before Hatate sent a shot wide from distance. Looking for a grandstand finish on his 100th European game as a manager, Brendan Rogers made a double change.
The Scottish side refused to give up, with Idah forcing a save from a tight angle, minutes before Schmeichel denied Rogers from close range.
An entertaining battle ultimately ended with Villa on top, as Watkins stole possession in the box and teed up Rogers for his first senior hat-trick.
Thanks to results elsewhere, Unai Emery’s side will progress straight to the round of 16, while Celtic will be in Friday’s play-off draw.