The men, Glenn Taylor, Dave Hill and Dylan Taylor, posted a video of Glenn pushing on the mushroom-shaped boulder, knocking it onto the valley ground below.
"Some little kid was about ready to walk down here and die and Glenn saved his life by getting the boulder out of the way," the cameraman is heard saying. "So it's all about saving lives here at Goblin Valley."
As the rock tumbled over, the three men shouted and laughed, giving each other high fives.
Glenn told the Salt Lake Tribune he knocked the boulder over because he was afraid it was a public safety hazard.
"I put my hand on a rock and moved," he said. While we were sitting right there we thought, 'Man if this rock falls it'll kill them.' I didn't have to push hard."
Park officials launched an investigation into the incident and the Emery County district attorney's office is assisting.
The men could face class B misdemeanor or second-degree felony charges.