Bogdan Stancu (18th minute) converted a penalty to hand Romania an early lead before Admir Mehmedi (57th) restored parity for the Swiss in the second half.
The result puts Switzerland at the top of Group A with four points after two matches. Romania are third with one point, two behind hosts France.
Romania had produced a spirited fight in the 1-0 defeat to title favourites France in their first match. The East Europeans repeated a similar spirited fight against the more skillful Swiss who were high on confidence having started with a win over Albania.
Switzerland dominated most of the match and much of the action was confined to the Romanian half.
Romania were forced to defend tooth and nail but a fast counter saw Stephan Lichtsteiner bring down Alexandru Chipciu inside the Swiss penalty area. Stancu stepped forward to smash home the resultant penalty and give Romania the lead.
Switzerland continued to dominate possession with Romania sitting back in defence. They were finally rewarded for their persistent aggression when Ahmedi slammed a loose ball into the net to salvage a point.