Ecuador, who finished second in South American qualifying, had 28 shots, including 15 on target but Room stood firm in an astonishing display in Kansas City.
His 15 saves are the most on record, since 1966, by any goalkeeper a World Cup match that did not feature extra-time.
World Cup debutants Curacao, the smallest nation by population ever to qualify for the tournaments, slumped to a 7-1 defeat against Germany in their opening match but restored pride in the American Midwest.
Ecuador fans turned the Arrowhead Stadium, the home of NFL team Kansas City Chiefs, yellow, hugely outnumbering supporters of Curacao.
But Curacao had royalty on their side in the form of Dutch King Willem-Alexander and Queen Maxima.
The island is an autonomous country within the Kingdom of the Netherlands.
Out of their 26-strong squad, managed by vastly experienced Dutch coach Dick Advocaat, 25 were born in the Netherlands, and most play their football there.
The match started at a fizzing pace.
Ecuador seemed certain to open the scoring in the third minute when former West Ham forward Enner Valencia burst through the middle but Room tipped the ball around the post.
Sherel Floranus fired over at the other end as Curacao showed their pace on the break.
Valencia failed to beat Room from close range before Jordy Alcivar had an effort as Ecuador continued to dominate possession.
The South American team ended the first half with 65 percent of possession but nothing to show for their dominance.
They went close to breaking the deadlock just before the hour mark but Room kept out a Gonzala Plata header, before a flurry of Curacao chances.
Ecuador, more than 50 places higher than Curacao in the Fifa rankings, looked increasingly frazzled as they pressed for a goal.
As the match neared its end, chances continued to come thick and fast but Room stood firm.
Ecuador substitute Angelo Preciado mishit a cross that bounced off the top of the crossbar and went behind.
The Curacao players swarmed around Room at the end of the match, celebrating an extraordinary point.
Earlier, German’s victory over Ivory Coast 2-1 in Toronto, ensured their qualification for the round of 32.
Curacao’s draw ensures Germany will now top the group.
Ecuador will play Germany on Thursday while Curacao take on Ivory Coast. (AFP)