The visitors had the first chance of the evening on five minutes but Leon Bailey’s header lacked conviction.
Yet, just three minutes later, two Monaco players showed the Jamaican international how it is done. From a corner, Thilo Kehrer's bullet header was well stopped by Emiliano Martínez but Wilfried Singo reacted quickest to nod home the opener.
Villa’s Argentinian stopper was called into action shortly after to deny Maghnes Akliouche but the tide of pressure would turn soon after.
After Radosław Majecki clung on to a Lucas Digne free-kick, Emiliano Buendía started pulling the strings. First, his ball intended for Ollie Watkins found Bailey, who forced Monaco’s Polish keeper to tip over the bar.
Buendia – making his European debut – then did pick out Watkins in first-half stoppage time but Majecki diverted it around the post.
That wasn’t the last chance of the first half though, as Akliouche blazed over with the last kick when he should have done better.
After Morgan Rogers spurned a chance to kick off the second half, it looked as though it was third time lucky for Akliouche as he swept home a defence-splitting pass from Vanderson. However, the French Olympian had mistimed his run and was flagged offside.
The game soon transitioned into an end-to-end encounter with nervy moments at both ends, albeit without either goalkeeper being stretched.
Unai Emery introduced Jhon Durán just before the hour mark to play alongside Watkins but it was an unlikely source who came close to an equaliser 10 minutes later as Matty Cash flashed an effort across the face of goal.
It was a replacement introduced by Adi Hütter who had a good chance to double the hosts’ lead but Tyrone Mings produced a remarkable block on Aleksandr Golovin’s goal-bound effort.
Ultimately, the victory snaps a four-game winless run and marks just a third win in their last 10 games for Les Monégasques, who visit 2023 runners-up Inter Milan next.
Meanwhile, Villa’s border battle with Celtic on matchday six will be crucial for their automatic qualification hopes.