Having ended the "wild west sideshow" method of capital punishment in 2004, the state's legislators have been debating the option since December as an "execution backup" if lethal injections cannot be obtained.
Following an 18-10 vote in the State Senate, the bill still needs the approval of Governor Gary Herbert, who has the constitutional power to veto the law.
Gov. Herbert, a Republican, has not made it clear whether he will sign the bill into law or veto it.
"If those substances cannot be obtained, this proposal would make sure that those instructed to carry out the lawful order of the court and the carefully deliberated decision of the jury can do so," he said.
"Our state, as is the case with states around the country, is finding it increasingly difficult to obtain the substances required to perform a lethal injection.
"We are dedicated to pursuing all reasonable and legal options to obtain those substances to make sure that, when required, we are in a position to carry out this very serious sentence by lethal injection."
State congressman Paul Ray authored and sponsored the bill, citing firing squad as the next most humane death penalty.
"Any form of death is obviously a serious subject, so the two reasons I chose it were, obviously, No. 1, that’s what we’ve done in the past, and secondly, out of all the other options, it is the most humane," Ray told the Los Angeles Times.
"We can either revert to the firing squad and get it taken care of, or we can spend millions of dollars trying to mitigate lethal injection."
A similar bill failed to pass the Wyoming state legislature earlier this year.
Other states using the death penalty have also been hit by the drug shortage, which has largely been caused by the European pharmaceutical manufacturer ceasing the sale of pentobarbital to US prisons on ethical grounds.
California, Florida, Ohio and Georgia are also considering other methods, with Arkansas legalising the use of firing squads earlier this year.
Oklahoma have also been weighing up their options following the botched lethal injection of Clayton Lockett. The convicted rapist and murderer writhed and convulsed on the execution table, taking 43 minutes to die, because a substitute drug, midazolam, had been used in place of pentobarbital.
In a more recent case, the execution of Kelly Renee Gissendaner was delayed due to a "cloudy" drug.
Lethal injection has long been considered the most humane and painless way to carry out an execution, but several failures in recent years have pushed lawmakers to consider other avenues, although no states have considered repealing the punishment altogether. Tennessee reinstated the electric chair but death row inmates sued to block its use.
A law change in 2004 made lethal injections the automatic default method of state-sponsored execution in Utah, with firing squad only remaining legal as a constitutional fail-safe.
But prisoners sentenced before then were still able to choose firing squad as their method of execution, the last case being the lawful killing of Ronnie Lee Gardner in 2010.
Gardner apparently chose firing squad because he hoped it would stir up controversy and a debate about capital punishment.
If Rep. Ray's bill is signed into law, prisoners will not have the choice, firing squads will be used by default if the appropriate lethal injection drugs cannot be secured 30 days before the scheduled execution date.
"It's not humane at all," Gardner's brother Randy told NBC. "I got to see the four bullet wounds in my brother's chest after the execution and I could have put my hand in there. It's cruel and unusual punishment for sure."