The “Boyhood” star, who who is dad to daughters Clementine, 6, and Indiana, 3 (and also has two older kids, Maya, 16, and Levon, 12, with ex-wife Uma Thurman), explained to Fallon that singing lullabies unaccompanied wouldn't cut it. He had to do it while strumming guitar, and while singing in a Dylan voice.
Hawke, 44, then went on to show the host what he meant — starting with a fantastic rendition of "Rock-a-Bye Baby" complete with perfect Dylan-esque snarl.
Next, Fallon pulled out the guitar he just "happened to have" and proceeded to sing his daughter, Winnie, 20 months, a "Twinkle Twinkle" tune, just in case she was watching and struggling to drop off to sleep.
The audience loved Fallon's attempts, but Hawke was more criticial, saying Fallon was too upbeat in his singing.
Watch the video above to see the duo sing their ultimate Dylan-style duet, "Hush Little Baby!"