A second-half goal by Admir Mehmedi earned a point for Switzerland at the Parc des Princes stadium, Paris.
Romania took an early lead after Bogdan Stancu netted an 18th-minute penalty, following a Litchsteiner foul on Chipciu. Stancu stepped up and confidently dispatched the penalty, sending Yann Sommer the wrong way.
Despite the Swiss dominating the game, Romania came close to doubling their lead in the 28th minute when Sapunaru hit the post from 6 yards out.
However, the Swiss continued to press and found their deserved equaliser in the 57th minute. A stunning Admir Mehmedi flew into the net following a deflection from a Ricardo Rodriguez corner.
The match remained level, with Switzerland edging closer to qualifying for the knockout stages. The Swiss will play France on Sunday, with Romania facing Albania on the same day.