The Germans, who moved into the last 16 for the second consecutive season, took a deserved lead in the 51st minute through 20-year-old Draxler after dominating from the start and needing victory to advance from Group E.
They were lucky to have had their second goal count, however, with at least four Schalke players clearly in offside position when Matip slotted in from close range to seal the win and relieve some of the pressure on coach Jens Keller.
The win moved Schalke, who have dropped down to sixth in the Bundesliga, above their Swiss rivals into second place with Chelsea securing top spot in the group.
Schalke, who had not won any group game since beating Basel on matchday two, carved out their first chance in the 12th minute with Taulant Xhaka sending his clearance on to the crossbar and teenager Max Meyer seeing his rebound shot cleared on the line.
Jefferson Farfan picked up the ball in the box but sent his curling shot narrowly wide as Schalke pressed high in the Basel half.
Things took a turn for the worse in the 31st minute for the Swiss, whose last trip to Germany was a 7-0 demolition by Bayern Munich two seasons ago, when Ivan Ivanov was sent off for a foul on Adam Szalai who was charging clear at the edge of the box.
The Hungarian forward had come on seconds earlier for injured captain Benedikt Hoewedes as coach Jens Keller, under mounting pressure to turn things around, brought on a striker for a central defender.
Germany international Draxler and 18-year-old Meyer continued to wreaked havoc with their dazzling display of tight dribbling and explosive speed but Farfan failed to stab in from close range in their biggest chance before the break.
Draxler managed to break the deadlock five minutes after the restart with Farfan delivering a cross at the far post and the 20-year-old drilling in.
Matip then was left in the box along with three other Schalke players but neither official signalled for offside and the Cameroon international had little trouble in scoring.
The Swiss side will go into the Europa League.
- Sports & Recreation
- Jefferson Farfan