The 17-year-old singer and actress made her late-night TV debut during Thursday's episode of the NBC series.
Rodrigo sang and played piano while illuminated by a spotlight that appeared to encase her in light. She was accompanied by live instrumentalists.
"so surreal. thx a million @jimmyfallon," Rodrigo tweeted after the episode.
Rodrigo released "Drivers License" in January. Many fans believe the song addresses a love triangle between Rodrigo, her High School Musical: The Musical: The Series co-star and rumored ex-boyfriend Joshua Bassett, 20, and actress and singer Sabrina Carpenter, 21.
In "Drivers License," Rodrigo sings about missing an ex who has moved on with an older, blonde girl. Carpenter subsequently released the song "Skin," but said in January that "Skin" isn't calling out anyone in particular.
"the song isn't calling out one single person," she wrote on Instagram. "some lines address a specific situation, while other lines address plenty of other experiences I've had this past year."
Bassett sings about a lying ex and the karma that will leave them "drowning in regret" in the new song "Only a Matter of Time," released last week.
Rodrigo's "Drivers License" debuted at No. 1 on the Billboard Hot 100 following its release.
Rodrigo and Bassett play Nini Salazar-Roberts and Ricky Bowen on High School Musical: The Musical: The Series, which airs on Disney+. Carpenter starred on the Disney Channel series Girl Meets World.