Draxler netted the winner in the second half of a game which was halted after only four minutes when the protesters abseiled down from the roof of Basel's St Jakob-Park stadium.
Spanish referee Alberto Mallenco halted the game after the protesters unfurled a banner which contained a message against Schalke sponsor Gazprom.
The banner was removed and Mallenco resumed proceedings after a short delay. The protesters were removed from the roof and were arrested by police.
UEFA later confirmed that disciplinary action might be taken against Basel over the protest but only after the match delegate's report has been submitted.
The visitor threatened again but when Atsuto Uchida crossed
Draxler was off target for Schalke after bringing down a cross and making room for his shot.
Schalke continued to dominate the first half and with 30 minutes gone could have threatened again but for some poor control in front of goal.
A fine move by the away side split the Basel defence but poor control by
As Basel began to come more into the game as half-time approached Schalke picked up two yellow cards in quick succession.
Dennis Aogo was the first to be booked for a foul on Mohamed Salah and then Farfan was cautioned by referee Mallenco for his foul on
Five minutes before half-time Basel forced a rare corner but an inswinging delivery from the left by
Schalke suffered a blow just before half-time as Farfan limped off injured and was replaced by
Basel's Ivanov tried a speculative shot from distance but his effort was off target.
Draxler crossed for Szalai but his header was saved by
Schalke pressed its superiority and took the lead after 53 minutes when Draxler fired a 20-yard volley into the top right corner of the goal.
Draxler tried to add a second late on but the visitor had already done enough to secure all three points and go top of the group.