"I looked at the linesman, he made no move and I just played on," the defender said.
Matip collected a free-kick from Jefferson Farfan and had no trouble slotting home with no Basel defenders anywhere near to challenge him.
Basel defender Ivan Ivanov was sent off in the 31st in a harsh decision by referee Paolo Tagliavento. Ivanov pulled down Adam Szalai just outside the area. Schalke's Benedikt Hoewedes escaped with a yellow card for a similar foul only minutes earlier.
Hoewedes pulled a hamstring in that challenge and had to be substituted. Szalai came in and earned the decisive foul with his first action, although he may have been offside as well.
Farfan had also set up Schalke's first goal, sending a long ball to the far post for Draxler to send a first-time low shot past the wrong-footed Basel goalkeeper Yann Sommer. Draxler later also limped off the field.
Basel came into the match riding an 11-game unbeaten run and would have advanced with a draw. Schalke needed to win to progress and the victory gave Keller some breathing room.
"We were under a lot of pressure and I must compliment my teammates," Schalke's Kevin-Prince Boateng said.
Farfan tormented Basel's defense from the start and curled a shot wide in the 17th, while Sommer turned away Farfan's stab from close range in the 44th.
Early in the match, Taulant Xhaka had redirected a cross from Farfan onto his own crossbar.
Sommer made a brilliant save on Farfan's free kick in 82nd, digging out the ball from upper right corner, then denied the Peruvian with another outstanding save late in the match.
Farfan finally beat Sommer but hit the post in the 89th.
