Nearly 15 million households tuned in to see Robinson humiliate failing contestants, in a five-year record for US network NBC, beating rivals CBS and Fox TV in its timeslot.
It confounded critics who had given it a lukewarm reception.
There was some praise for the show itself - but little for Robinson, who was accused of failing to live up to her dominatrix reputation and being difficult to understand.
But off-set Robinson hit back at those who panned her performance.
The New York Post reported she had called their television critic Adam Buckley "an old fart" after he slammed the show.
She continued: "Your critic, I really wanted to talk to him. Is he out of jail on day release?
"I don't really care what he says. I'd rather have my earnings than his."
And when the newspaper's reporter asked her to repeat what she had just said, Robinson responded tersely.
"Didn't they teach you shorthand in school? You are the weakest link," she said.
Compelling
Robinson kept her stern demeanour throughout the first hour-long edition - including her catch phrase: "You are the weakest link - goodbye".
But it was not a format which won many fans among the American TV reviewers.
You could not help but watch it
The influential New York Times observed of Robinson: "Her manner has been described as that of a dominatrix.
"But with her practical cropped hair and glasses, she is more like a school librarian in a black leather coat."
The LA Times TV critic, Howard Rosenberg, described the British import as "somewhat entertaining".
"I think her humour is kind of cheap - it is the cheap shot," journalist Melanie Seymour told the BBC.
But USA Today said: "If this entertainingly hard-edged English import takes off like NBC thinks it will, that phrase likely will spread like foot-and-mouth disease so brace yourself."
Among the millions who tuned in was John Sullivan from Granada Hills, California.
He said: "I thought it was brutal. She turned everybody on everybody else.
"You could not help but watch it."
The British newspaper, The Sun is reporting that Robinson is under armed guard in America amid fears for her safety.