QVC's viral wig-mogul Tori Brattin is reacting to all the love she's received since her on-air blooper, describing the moment Jimmy Fallon called to invite her on "The Tonight Show."

Toni hopped on the "TMZ Podcast" and caught up with TMZ's Alexa Klohn to chat about their interview last week ... where the TV personality pitched one of her viral wigs to the late night host -- who saw our clip and wanted to try on one of the wigs himself.

Brattin tells us when QVC called to tell her Jimmy's team had reached out, she immediately ran up the stairs, grabbed a ton of her iconic wigs, threw them into her suitcase, and made her way to NYC for Monday night's show.

Even after 30 years of on-air action, Toni says she was extremely nervous and never believed saying "blowjob" accidentally would land her such an amazing gig ... holding back tears as she describes what it was like having her kids and family in the audience watching her shine.

As we previously reported ... the NSFW moment came as Toni was showing off one of her stylish hairpieces ... walking viewers through its texture and wave pattern when things took a turn. She told viewers, "It looks like you went and got a blowjob at your -- a blowout at your salon."

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According to Toni, the network was kind about the mishap -- her professionalism blew them away.