Brooks, 57, took on the music legends for host Kelly Clarkson and discussed his favorite songs to cover in the interview.
"I think it's the stuff that they're not expecting," Brooks said. "I'm the last of six kids, mom and dad had their different tastes. So yeah, you're gonna hear George Strait, you're gonna hear [Sammy] Hagar, but you're also gonna hear [Otis Redding]."
Brooks covered Taylor's song "Fire and Rain" before harmonizing with Clarkson on his own song "The River," which is inspired by Taylor.
Clarkson started crying during Brooks' cover of Dylan's song "Make You Feel My Love."
"If you would have told me as a kid that that moment would have happened? I'm sorry. I just can't believe my life sometimes, that you're just sitting here serenading me," Clarkson said.
In addition, Brooks discussed his wife, country music star Trisha Yearwood, and his daughters, Allie, Taylor and August, with Sandy Mahl. Brooks said Yearwood and his daughters also exchanged rings during their wedding.
Brooks said on Jimmy Kimmel Live! last week that his 14th studio album, Fun, is complete. The album includes Brooks' single with Blake Shelton, "Dive Bar." Brooks is in the midst of his Dive Bar tour and said his early dive bar shows were a "sweet" but dangerous experience.
"Then, nobody was there," the singer said. "You'd have one single -- 90 minutes, one single. You'd play it like three or four times a night and each time they'd act like it's the first time they heard it. It was so sweet."
"Now you go in there, and thank God they're packed. You've got a list about this long," he added. "They know every word, so you start it, they finish it. Start the next one, they finish that one. Easiest gig on the planet."
Brooks recalled an early gig in Southern Oklahoma where the venue ended up burning down.
"It's a honky-tonk. Everybody's in danger," Brooks said. "We brought some buddies from Northern Oklahoma. Somewhere around two or three songs in, the fight starts ... The next thing you know, the whole damn place is burning. The thing burned down to the ground.
"We didn't get paid that night," he added with a laugh. "That was another day on the tour, man."