It was 1967 and de la Parra had immigrated to the United States from his native Mexico City and was playing in a funky little place called The Tom Cat Club in Torrance, Calif.
The young drummer showed up at the audition with his drumsticks and a blues album recorded by Junior Wells and Buddy Guy.
"I didn't know the guys in Canned Heat were blues records collectors," de la Parra said during an interview from his home near Santa Barbara, Calif. "I just showed up with the record because I bought it on the way to the audition."
A few years later, the band's late lead singer Bob "The Bear" Hite told de la Parra that the record got him into the band.
"He said, 'We already knew you were a good drummer, but when I saw you in that door with that record under your arm, I knew you were going to be the drummer for Canned Heat,'" de la Parra said. "It was amazing to me that I showed up with my accent, hardly knowing any English, but he saw the record, which I had just bought on the way to the audition."
That was the beginning of a long musical career for de la Parra, who will bring Canned Heat to the Egyptian Theatre on Feb. 8 and Feb. 9. The band is known for the songs "Going Up the Country," "On the Road Again" and "Let's Work Together."
Since joining Canned Heat, the drummer has seen waves of success, including a definitive performance at the original Woodstock Music and Art Fair in 1969, and waves of tragedy, such as the death of lead singer Bob "The Bear" Hite in 1981.
In fact, the band's ups and downs inspired de la Parra to publish a biography called "Living the Blues" in 2011.
"I go into detail about all the different things we had been through," de la Parra said. "And we really have been through a lot."
Still, de la Parra is still committed to bring the band's musical experience to audiences around the world.
"I do feel responsible for keeping the band going and I do it because Canned Heat was a very precious thing in my life," he said. "I appreciated the fact that I came to America as an immigrant and joined this famous band. I may have given it more value than the other guys because they were used to it, but to me it was a major thing."
The drummer said Canned Heat is his "life's train."
"In life when you see things go by, you need to made some decisions and jump on one of them," he said. "When they offered me the job, I said, 'I was born to play with Canned Heat,' because I felt that commitment. I liked the band and I liked the members of the band."
de la Parra said while he has been fortunate to play music for a living, the lifestyle has been a constant uphill battle.
"We had three years of extreme fame in one of the best periods of history of music in the late 1960s and early 1970s," he said. "We have stayed true to what we do and not prostitute the band to be famous even when the other trends have come in and out over the years. And we are also honest about that."
The honesty didn't allow the band to conform to music trends, so, unfortunately, during the late 1970s and early 1980s, it hit a dry spell that ultimately contributed to Hite's death in 1981.
"Bob died, he was in a sad place, because he couldn't pay the electric bills or take care of his family," de la Parra said. "It wasn't like when (guitarist) Alan (Wilson) died in 1970. When Alan died, we were very popular, but when Bob died, it was different."
Hite's death nearly disbanded Canned Heat, but de la Parra left it up to the fans to decide whether or not to keep it going.
"When Alan died, we knew we were going to keep the band going no matter what, because it was still fresh," he said. "But when Bob died, he was the image. He was the front man, 'The Bear.'"
de la Parra remembered crying with the band's former guitarist Henry "The Sunflower" Vestine.
"We had booked a tour in Australia before Bob died and we didn't know if we were going to tour," de la Parra said. "But we got a call from the promoter and he said the Australian will accept the band if you still come with another lead singer.
"So, we went to Australia and, all of sudden, we were famous again."
These days, the band is still trucking on and in 2007, de la Parra reunited with guitarist Harvey "The Snake" Mandel and bassist Larry "The Mole" Taylor.
"The line up coming to Park City is as original as possible," de la Parra said. "While Harvey wasn't the band's original guitar player, he came into the band right before we played Woodstock. So, basically, you're getting the Woodstock lineup, with the exception of vocalist Dale Spalding."
Spalding, who hails from New Orleans, is a fantastic lead singer, de la Parra said.
"We can't wait to come, because February 8 is my birthday, and I love to celebrate and entertain," he said.
The Egyptian Theatre, 328 Main St., will present the classic-rock and blues of Canned Heat on Friday, Feb. 8, and Saturday, Feb. 9, at 8 p.m. Tickets range from $25 to $45 and available at www.parkcityshows.com.