But her awkward moment also had a second act.
Exelby had been gazing at a pen in her hands, unaware she was live, when a broadcast cut back to her in an Australian Broadcasting Corp (ABC) studio.
She gave an alarmed reaction when she realised the error, but settled quickly to read the next story.
A clip of the blooper was widely shared online, with most observers appearing to sympathise with Exelby. She addressed the subject in a tweet.
The saga might have ended there, but on Monday night, Sydney's Daily Telegraph reported Exelby had been sidelined from her newsreading duties.
It did not quote the ABC, but a spokesperson soon told local media: "Natasha Exelby is a casual contributor, not a staff member. She has been booked for occasional on-air shifts when needed, and also does other occasional shifts for the ABC News channel."
Commentators noted the ABC did not directly address whether Exelby had been benched, fuelling a backlash online.
Opposition Leader Bill Shorten and actor Russell Crowe were among many who criticised the report.
"Give her a break," one of Mr Shorten's senators, Sam Dastyari, told Fairfax Media.
"The idea that someone would be punished for what is a very innocent mishap is extraordinary."
It was not long before a petition began calling on the ABC to "reinstate" Exelby.
Other journalists began telling their own embarrassing stories in solidarity, many under the hashtag #PutYourBloopersOut.
The Project, a light-hearted news programme on another network, also joined in.
On Tuesday, ABC Director of News Gaven Morris denied Exelby had been punished, but said she was not currently scheduled for any news reading shifts.
"Media reports that Natasha has been 'banned', 'barred' or 'fired' are untrue," he said.
"While she is not currently doing any on-air shifts, this will be subject to normal performance management. I have spoken to Natasha and conveyed our regret that this has attracted such attention."
The broadcaster was committed to offering Exelby "various shifts" in the future, he said.