That's when the prolific singer-songwriter won best recording for children for his soundtrack of "The Muppet Movie," which included the popular song "Rainbow Connection."
Two years before that, in 1977, he took home his first Grammy for song of the year for Barbra Streisand's "Love Theme From A Star Is Born (Evergreen)." The song also netted Williams an Academy Award.
So where has Williams, now 73, been since then, and how did he end up speaking on behalf of a couple of French robots known as Daft Punk?
Williams rocketed to stardom in the '70s, co-writing hit songs with artists such as the Carpenters ("We've Only Just Begun"), Helen Reddy ("You And Me Against The World"), Three Dog Night ("An Old-Fashioned Love Song") and David Bowie ("Fill Your Heart").
Throughout the '70s, he was also a frequent guest on "The Tonight Show Starring Johnny Carson" and appeared on shows such as "The Love Boat," "Hawaii Five-O" and "The Gong Show." On the big screen, he starred in the films, "Smokey and The Bandit," "The Muppet Movie," Brian De Palma's "Phantom of the Paradise."
"If you look at my life you'll see that I was all over the place in the '70s," Williams told Grammy.com in 2012. "[I had] an amazingly productive, abundant career. And then in the '80s, all of the sudden I'm gone. What happened? What happened is, [as] I describe very succinctly in the film when a fan asked, 'I got drunk.' What happened is my addiction to the attention I was getting was outrun by another addiction."
The film Williams was referring to was the 2012 documentary "Paul Williams Still Alive," which charted his rapid rise to fame and his downfall to substance abuse followed by his road to recovery and more than two decades of sobriety.
But it was another film, the now cult classic "Phantom of the Paradise," that led to Daft Punk and their album "Random Access Memories."
"They'd seen it about 20 times. I think there's a chance that they got the idea to work behind the masks from that," he told ABC Radio.
Williams said Daft Punk "asked if I'd write lyrics to a couple of songs, which I did," adding, "Then, surprise of all surprises, they asked if I would sing 'Touch,' which is one of the songs on the album, the one I performed. The other one is 'Beyond,' which they performed."
He added, "It's the biggest album that I've been involved with in years and years and years. It's a great surprise."
It's also one that he's enjoying in his seventh decade.
"For one thing I'm 23 years sober so I get to remember how this one feels," Williams told ABC Radio.
"I think there's something about the fact that they have also reached out to some songwriters of my age," he said. "They have proved the opposite of ageism. They have said, 'This is something the world may really like.' Turns out they were right."
ABC Radio contributed to this report