Victory for the Swiss would have seen them qualify from Group A in either first or second position, but a spirited Romania performance ensured that the points would be shared in the French capital.
© Getty Images
The first serious chance of the match arrived in the sixth minute when Haris Seferovic found space inside the Romania box, but the Swiss striker could only curl his effort wide of Ciprian Tatarusanu's post.
Ten minutes later, Switzerland and indeed Seferovic had another chance after Xherdan Shaqiri had sent the forward away with a through-pass, but Tatarusanu was on hand to make a smart save.
Romania were awarded a penalty in the 18th minute, however, when Stephan Lichtsteiner pulled the shirt of Alexandru Chipciu inside the box, and Bogdan Stancu stepped up to score his second spot kick of the competition.
Switzerland were almost on terms three minutes later when Fabian Schar struck one from distance, but Romania's goalkeeper tipped the number 22's effort over the crossbar.
The end-to-end period of the match continued as Chipciu curled one just wide of the target and moments later, Cristian Sapunaru turned inside the Swiss box and released a strike, only to see the ball smash off the post.
Switzerland had a wonderful chance to draw level in the 38th minute when Lichtsteiner found the head of Blerim Dzemaili with a cross from the right, but the midfielder somehow missed the target from close range.
Less than one minute into the second period, Romania came close to scoring a second as Ovidiu Hoban met a loose ball inside the Switzerland box, but the defender's effort was always moving away from Yann Sommer's goal.
Romania again came close in the 52nd minute when Gabriel Torje delivered a dangerous cross from the right, but Swiss centre-back Johan Djourou, on the stretch, just about did enough to turn the ball behind for a corner.
Switzerland levelled the scores in the 57th minute, however, when Admir Mehmedi found the corner of the net with a powerful strike after Romania had failed to deal with a corner from Ricardo Rodriguez.
Needing a second to book their spot in the last-16 stage of the competition, Breel Embolo was introduced for Switzerland and the reported Manchester United target caused all sorts of problems with his pace and power in the final third.
Embolo met a deep cross from Lichtsteiner in the 68th minute as Switzerland came close, but the youngster's header just missed the post during a period where Romania were struggling to keep hold of the ball.
Shaqiri failed to make the most of a 25-yard free kick as Switzerland continued to threaten, before Dzemalli fired over the crossbar from distance 15 minutes from time.
The pressure from Vladimir Petkovic's team continued into the latter stages as Switzerland attempted to secure their spot in the next round, but they could not score a second against a well-drilled Romania outfit.
Next up for Switzerland is a clash with hosts France on Sunday, while Romania will take on Albania on the same night. Later this evening, France will attempt to book their spot in the round of 16 with a win over Albania.