Police in Rio Rancho, a northwest Albuquerque suburb, said the balloon got tangled in the line at about 8:30 a.m. When the passenger reached out to free the balloon, he was shocked, festival spokesman Tom Garrity said.
The balloon was freed, but the gondola crashed to the ground.
Rio Rancho police identified the pilot as Mark Kilgore, 59, of Albuquerque, and the passenger as Daniel Lovato, his 66-year-old crew chief.
KOB-TV reported that Lovato suffered serious burns on his face, chest and arms and underwent surgery at the University of New Mexico Hospital while Kilgore was treated for burns to the side of his face.
Although photos from the scene showed flames, Garrity said it was unclear if the gondola caught fire.
"We know there was arcing of electricity," he said. "We are still trying to figure out the specifics."
Rio Rancho police spokeswoman Janet Garcia said pictures showed some burns along the top of the gondola, but it did not appear that the gondola went up in flames.
Pamela Correa, general manager of the nearby Ask Academy, told the Albuquerque Journal she was in a morning meeting when she saw the balloon smoking about a quarter-mile down the hill from her building.
"I saw the balloon coming down. It looked like it was going to land," she said.
But then the lights went out for a moment, and she said she saw the gondola was almost completely billowing with smoke.
"I could just see the blown-out piece and the smoke," she said, referring to the top of the balloon. "And you could tell that there was something wrong."
She said the balloon chase crew was there right away and emergency crews responded quickly.
"You've seen pictures of it when things go wrong," she said. "But I've personally never witnessed it until now."
On Saturday, the opening day of the nine-day festival of more than 600 balloons, a 61-year-old woman broke her leg during a hard landing.