The journalist, who has closely followed Rob's story with BBC Breakfast since he was diagnosed with motor neurone disease (MND) in December 2019, attended the ceremony alongside the sports legend and his family.
The film was nominated for the Authored Documentary gong, which was awarded to Lewis Capaldi's Netflix film, Lewis Capaldi: How I'm Feeling Now.
Taking to X, formerly known as Twitter, after the show, Sally reshared a post from Rob's former rugby club Leeds Rhinos, who thanked viewers who voted for the documentary. The post read: "A huge thank you to everyone who voted for Rob and his family, it was an incredible opportunity to talk about MND once again to even more people, congrats to all the team at @BBCBreakfast on the nomination, who have told the Burrow family story with so much love and respect."
Sharing the statement, Sally, who has become friends with the Burrow family, wrote: "There's only one Rob Burrow," adding a red heart emoji.
Fans rushed to the comments section to praise the star for her coverage of the story over the years, with one person writing: "Well done to you Sally, kept the momentum going for a great cause," while another added: "You're amazing, Sally."
A third person tweeted: "Well done Sally, that was a lovely thing to do for a wonderful family," while another added: "You all look a million dollars. Congratulations to everyone nominated."
The documentary, which first aired in October 2022, follows Rob and his family as he lives with MND.
At the time of his diagnosis, Rob, 40, was told that he may only have a year to live, two at the most.
Speaking about the documentary in a statement for the BBC, Sally previously said: "This film shares the brutal reality of living with motor neurone disease, not just for Rob, but the impact it has on his whole family and friends. What he is doing will have a lasting legacy for people diagnosed today and in years to come."
She continued: "The documentary is an unflinching look at life through Rob’s eyes. We see him fight daily for small victories that we might take for granted. Every breath is a battle. Every moment with his family is a win for them all. But he is as funny today as he was the first day I met him, when he was just one of the greatest rugby league players of all time. He is still that, and so much more."
Sally's night out at the NTAs comes after the TV star returned to the UK following a trip to Spain. The 52-year-old marked the holiday with a series of photos on Instagram, including a selfie of the star relaxing on the beach while donning dark shades and a fluffy white robe.
"There are no prawns left in San Sebastián. I think we have eaten them all," she wrote in the caption ahead of her return to BBC Breakfast. She added: "Back on the @bbcbreakfast sofa tomorrow from 6. Join us if you can x."