The Swiss had the first chance of the match. Ricardo Rodriguez found space on the left flank and floated a cross towards the far post and Kevin Mbabu rose highest but headed wide.
Wales responded in the 15th minute. Daniel James surged down the left-hand side and whipped in a cross towards the back post for Kieffer Moore whose header was brilliantly saved by Yann Sommer.
Five minutes later, Xherdan Shaqiri delivered towards the near post with Fabian Schar glancing his header downwards towards the bottom right-hand corner as Danny Ward saved with his feet.
In the 41st minute, Remo Freuler pinged the ball into Haris Seferovic, who thundered an effort inches over Ward's crossbar.
The Red Crosses broke the deadlock five minutes after the interval. Shaqiri's corner found Breel Embolo, who headed past Ward and into the bottom left-hand corner.
Moore equalised in the 74th minute. James played the short corner to Joe Allen, who delivered to the near post for the frontman to glances the header across goal and into the bottom left corner.
Switzerland thought they had restored their lead in the 85th minute, but Mario Gavranovic's effort was ruled out after consultation with VAR as the sides came away with a point each.