The Swiss side headed to Gelsenkirchen in second spot in Group E, trailing leaders Chelsea by a point and leading their hosts by the same margin.
But their cause suffered a setback in the 32nd minute when they had defender Ivan Ivanov sent off, and Schalke made the extra man count soon after the interval with goals from Julian Draxler and Joel Matip seeing them through.
The Royal Blues had a couple of sights of goal in the first quarter but failed to really trouble the visiting defence, Kevin-Prince Boateng seeing his shot blocked and Max Meyer's attempt cleared by Ivanov.
Schalke lost Benedikt Howedes to injury in the 28th minute, the defender replaced by Adam Szalai soon after being somewhat fortunate to only be booked for a foul on Marco Streller.
Basel's hopes took a hit just after the half-hour mark when Ivanov was shown a straight red card for a professional foul on Szalai, the referee deeming the defender had denied the substitute a clear goalscoring opportunity when the pair tangled in the air in pursuit of a long ball forward.
Boateng drilled a left-footed shot goalwards from 25 yards just before the interval as Schalke looked to make their numerical superiority pay and, although it flew narrowly wide, the home fans did not have to wait too much longer for the deadlock to be broken after the restart.
In the 51st minute, Jefferson Farfan provided the cross from the right and Draxler was on hand to calmly slot into the bottom-right corner from 12 yards.
Six minutes later Schalke made it 2-0, Matip springing the offside trap and controlling Farfan's free-kick on his chest before firing past Yann Sommer.
Europa League-bound Basel briefly threatened a bid to get back into the game but the best they could muster was a Streller shot which Schalke goalkeeper Ralf Fahrmann was more than equal to.
Sommer, at the other end, had to be alert to prevent a third Schalke goal 10 minutes from time, tipping Farfan's curling free-kick around the post.