The Germany international opened the scoring before a controversial second strike allowed the hosts to secure a knockout stage place at the Veltins Arena
The Germans came into Wednesday's clash at the Veltins Arena having won just one of their last five, but cruised past the Swiss team - which played the majority of the game with 10 men.
Basel's hopes of qualifying at Schalke's expense were dented on the half-hour as defender Ivan Ivanov was sent off for hauling Adam Szalai down as the Hungarian closed on goal.
Julian Draxler showed his finesse to put Schalke ahead, turning home first-time from Jefferson Farfan's cross, though the German side's second goal was highly controversial.
Farfan came into the game on the back of scoring five in his last six outings, and played up top for Schalke alongside Draxler and Kevin-Prince Boateng, while Max Meyer replaced the suspended Jermaine Jones in midfield.
The Germans should have taken the lead on 11 minutes as Farfan launched a lightning counter down the right and crossed for Boateng. Taulant Xhaka was on hand to intercept, incredibly deflecting the ball onto his own crossbar before Draxler pounced on the loose ball and found Meyer, whose effort was hacked off the line.
The momentum swung even further in Schalke's favor just after the half-hour as Ivanov was softly dismissed for a tug on Szalai - introduced as a substitute for injured captain Benedikt Howedes.
Sommer got behind Farfan's resulting free-kick and then produced a stunning close-range stop from the Peruvian to keep the scores level at the break.
Schalke did not have to wait long to break the deadlock though, as Draxler slotted home just six minutes into the second half.
The Germans went two goals to the good seven minutes later, to the fury of Basel players and coach Murat Yakin.
Basel's defense sprung an offside trap from a right-wing Schalke free kick, but the linesman did not raise his flag, leaving Joel Matip all alone to slot home - although replays showed the Cameroonian was one of four home players beyond the last defender.
Szalai headed a good chance straight at Sommer, but there was concern for Schalke as Draxler was forced off with a hamstring injury.
Sommer made five saves of the highest order to cap a fine performance in defeat, but it was Schalke smiling at the final whistle after sealing a spot in the last 16.
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