Check out the clip ... the chart-topper wrapped up a pitch-perfect performance of Édith Piaf's classic, "Hymne A L'Amour," where she wore a sparkling silver gown that contrasted the golden glow of the floating Olympics cauldron beside her.

Celine's particularly impressive here ... looking so much like her vintage self it's a shock to remember she's suffering from Stiff-Person Syndrome -- a major neurological disorder.

We've told you all about Celine's run-up to the Olympics ... from confirming she was going to take the stage for the first time in years to capturing the frenzy of fans waiting for her when she left her hotel Thursday night.

Remember, a local French reporter announced Celine and Lady Gaga would be collaborating for a duet earlier this week ... leaving fans eager for the opening ceremony. However, this reported number didn't come to pass ... as Gaga kicked off the show with a rendition of Zizi Jeanmaire's "Mon Truc En Plume." Celine carried her portion all on her own.

Dion promised in her documentary "I Am: Celine Dion" to crawl to the stage if she had to in order to keep performing ... and based on how she did tonight, she certainly meant it.