The result lifted Schalke above Sporting Lisbon into second place after the Portuguese side, needing a draw at Chelsea to progress into the last 16, were beaten 3-1 by the group winners.
Meyer pounced just after hour mark, six minutes after replacing the ineffective Tranquillo Barnetta, when Maribor keeper Jasmin Handanovićc failed to clear a low cross by midfielder Marco Hoger.
Schalke dominated possession in the first half but Maribor, roared on by their 12,000 home fans who lit flares midway through the opening period, looked more dangerous on the break.
The home side came desperately close in the 23rd minute, when Schalke's Japanese right back Atsuto Uchida cleared a Željko Filipović header off the line and blocked the follow-up from Brazilian striker Tavares.
The scare spurred the visitors into action and Dutchman Klaas-Jan Huntelaar blazed his shot wildly over the bar after turning his marker superbly on the halfway line and racing through on goal.
Huntelaar and strike partner Eric Choupo-Moting were starved of service up front with Maribor's packed midfield cutting off the supply routes and their back four holding firm.
But the German side missed a gilt-edged chance shortly after halftime when Huntelaar's close-range shot hit the inside of the far post and Aleksandar Rajcevic cleared the ball off the line.
Schalke piled the pressure and punished the hosts as their guard dropped, allowing Meyer to slip into the penalty box and sweep the ball into an empty net from 12 metres after Handanović's calamitous error.
The Slovenians, who needed a win to avoid finishing bottom and grab the consolation prize of carrying on in the Europa League, threw men forward in the closing stages but failed to trouble Schalke.
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