The 37-year-old Room made 15 saves - just one shy of the record 16 set by American Tim Howard in an extra-time loss to Belgium in 2014 since saves became an officlal World Cup stat in 1966.
He acted as a one-man barrier on Saturday, with Dick Advocaat's brave side bouncing back from their 7-1 thrashing by Germany in their opening game.
The point, a historic result for a tiny nation with just 158,000 people, keeps their unlikely hopes of advancing through Group E alive and they will progress to the knockout stages if they can somehow beat Ivory Coast in their final match.
The outcome also allowed Germany, who beat Ivory Coast earlier in the day, to clinch Group E.
It was all down to a monumental performance from Room, whose shutout of Jamaica last November sent Curacao to their first World Cup.
"It's going to be an insane memory," said Room, who plays for USL Championship club Miami FC.Â
"You don't think about it when you do it but of course it's going to be something you look back to. For me as a goalkeeper, this is almost a perfect game."
He was in action from as early as the third minute when he denied Enner Valencia with a brilliant save.
Room was on a one-man mission as he kept out Gonzalo Plata's effort while again denying Valencia with an impressive low stop.
Curacao had their moments, with former Manchester United midfielder Tahith Chong wasting a three-on-two situation while Juninho Bacuna had a shot blocked in the penalty area.
Advocaat's men had a triple chance to take the lead on the hour as Ecuador goalkeeper Hernan Galindez made a good double stop to deny Leandro Bacuna and Livano Comenencia before Moises Caicedo blocked Jurgen Locadia's follow-up effort.
But Room continued to keep his side in it as he denied Valencia and Kevin Rodriguez before Piero Hincapie sent a free header over and Plata somehow missed after bursting into the area.
Rodriguez then hit the crossbar with a cross-shot, but Room was the hero as the Caribbean nation held on for a historic result.
"I think I need a statue in Curacao now," he said with a smile.
The unexpected draw left Ecuador in a tough spot going into their clash with Germany on Thursday.
"Well, there are things you cannot explain in football," Ecuador coach Sebastian Beccacece said. "I am the one who bears responsibility, and I told my team, 'If you're giving it all, competing, I have no complaints.'
"As long as we are alive, we will continue to give it our all. We are very united. We are like a family. No one said it would be easy."
- with The AP
10°C