The couple performed the song from home on Sunday. Shelton played the guitar while Stefani wore a shirt that expressed her love for the country star.
"I don't wanna live without you/ I don't even wanna even breathe/ I don't wanna dream about you/ Wanna wake up with you next to me," the couple sang during the chorus.
"Nobody But You" appears on Shelton's 2019 compilation album Fully Loaded: God's Country. Shelton and Stefani released a music video for the song in January which featured the pair going on a date together.
Shelton told Fallon how he and Stefani are doing at home in Oklahoma during the COVID-19 pandemic as Stefani gave him a haircut.
"Literally, it's like Little House on the Prairie out here. She makes bread. I've been building a fence and gardening. We're pretty self-sufficient out here," Shelton said.