PSG had taken the lead with a Blaise Matuidi goal two minutes before halftime but Basel rattled the Ligue 1 champions when Luca Zuffi equalised out of the blue in the 76th minute.
In a dramatic finale the Swiss champions had midfielder Serey Die sent off for a second yellow card following a foul on Marco Verratti and could have snatched a win seconds before Meunier's strike.
PSG, quarter-finalists last season, have 10 points from four games in Group A alongside Arsenal, who also qualified. Basel have one point and were eliminated alongside Ludogorets.
PSG dominated the first half and went ahead when Meunier drove a fierce shot at goal which Matuidi flicked into the net from close range.
The visitors had enough chances to settle the game, but instead Zuffi collected a throw in around 30 metres out and launched a looping effort towards goal which flew over a startled Alphonse Areola and into the net.
Basel went agonisingly close to scoring a second when a free kick flew across the PSG goal and found Marc Janko unmarked at the far post, but he failed to make proper contact.
Seconds later, a PSG cross found Meunier who, having missed two easier chances, met the ball with a thumping volley which swerved past Tomas Vaclik and into the top corner.
(Writing by Brian Homewood; Editing by Toby Davis)
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