The eccentric pop singer had played a cover of the late songwriter's peace song at a Human Rights Campaign dinner in Washington DC, which Yoko attended.
She later wrote on her Twitter blog: "Dear Lady Gaga, Thank you for singing 'Imagine'.
"Hearing that made me choke up. You are so beautiful! In Sisterhood and love, Yoko."
Gaga changed the lyrics to the 1971 song in tribute to gay college student Matthew Shepard, who was murdered in 1998.
She sang: "Imagine there's no heaven/ It's easy if you try. No hell below us/ And only Matthew in the sky."
Shepard's murder, which it is claimed was due to his sexuality, brought international attention to the issue of hate crime legislation.
US President Barack Obama took to the stage ahead of the singer and joked about being on before Gaga.
He said: "It's privilege to be here tonight to open for Lady Gaga... I've made it."