Vladimir Petkovic's side finished behind Italy and Wales in their group and face an anxious wait to see if it will progress as one of the four best third-placed teams, although a superb display in Baku has put it in a strong position.
Haris Seferovic got Switzerland on its way early on from 20 yards before another fine strike from Xherdan Shaqiri put them two goals up at the break.
Irfan Can Kahveci pulled one back for Turkey, but Shaqiri wrapped up Switzerland's first win of the tournament – and ensured its opponent leave the competition having failed to pick up a single point – with another wonderful finish.
Despite Turkey's strong start, which saw Kaan Ayhan test Yann Sommer from distance, it was Switzerland who struck first, Seferovic lashing into Ugurcan Cakir's bottom-left corner after just six minutes.
Shaqiri doubled its advantage in the 26th minute, the Liverpool forward whipping superbly past Cakir from just outside the penalty area.
A smart save from Cakir denied a clean-through Shaqiri moments later as Switzerland threatened to run away with it, while at the other end Sommer kept out the impressive Mert Muldur on three occasions before the interval.
Switzerland continued to pour forward after the restart, with Cakir doing well to repel efforts from Breel Embolo and Seferovic, but Kahveci gave Turkey hope of a comeback with a sumptuous strike from outside the area after 62 minutes.
Shaqiri restored Switzerland's two-goal advantage six minutes later, though, the 29-year-old applying a clinical finishing touch to Steven Zuber's pass, the Eintracht Frankfurt midfielder becoming only the third player to register three assists in a single match at the European Championship.
Granit Xhaka struck the post late on as Switzerland sought in vain to overturn a goal deficit to second-placed Wales, settling instead for sending an insipid Turkey home with a whimper.