Vladimir Petkovic's men could have qualified for the knock-out stages for the first time with a victory in Paris, but fell behind to Bogdan Stancu's first-half penalty – Romania's second spot-kick of the tournament.
Admir Mehmedi brilliantly levelled the scores after the break, preventing Romania from recording just their second win at a European Championship.
Switzerland looked the more likely to win it from there, but failed to make their pressure count and will conclude their group campaign against hosts France.
Romania, meanwhile, will surely need a win in their match against underdogs Albania if they are to extend their tournament.
While Anghel Iordanescu made four alterations to the Romania team that valiantly lost to hosts France on the opening night, Switzerland were unchanged from their win against Albania, and Haris Seferovic, trusted to lead the line again despite missing a glut of chances last time out, had further opportunities early on.
Taking a pass in his stride and turning Vlad Chiriches in the sixth minute, the forward sent an effort flying past the far post, before shooting tamely at Ciprian Tatarusanu 10 minutes later.
And, this time, Switzerland were immediately made to pay for his profligacy.
With Stephan Lichtsteiner tugging Alexandru Chipciu's shirt in the area, Romania were awarded a penalty. As against France, Stancu took full advantage to find the net.
But there was almost an instant response.
Like Stancu, Fabian Schar had scored in his side's opener, and he almost caught Tatarusanu out with a stunning long-range volley, acrobatically tipped over by the Fiorentina goalkeeper.
Petkovic's side were soon close to being caught out again, though.
After Chipciu curled wide from a tight angle, right back Cristian Sapunaru should have done better as he prodded a loose ball against the post.
However, with Switzerland knowing a win would seal their progression, red shirts continued to pour forward, and Blerim Dzemaili inexplicably placed a free header off target from close range.
This Romania outfit had Europe's best defence in qualifying, and, given their pace on the counter, the Swiss appeared to be playing into their hands.
But, finally, with 57 minutes played, Mehmedi forged a breakthrough.
Ricardo Rodriguez's scrambled corner dropped onto his team-mate's toe, perfect for the Bayer Leverkusen forward to thump high into the net.
And Switzerland were not happy to settle for a point, introducing teenage superstar Breel Embolo from the bench.
The Basel youngster was a constant nuisance in the final half hour of the match, but Yann Sommer had to remain on his toes to repel a ferocious Gabriel Torje free-kick.
And for all the Swiss pressure, they struggled to create clear sights of goal in the closing period of the game.
Dzemaili flashed a volley over the top, but Romania were able to close the game out to keep their slim hopes of qualifying from the group stages alive.
