Rep. David Hogue, R-Riverton, implied such games played a serious role in school shootings such as Columbine.
"Would these same kids have done this anyway without watching violent videos? Maybe not." he said.
HB257, which passed 56-8, would add extremely violent "interactive video or electronic" games to the state's statute protecting minors from harmful material; the statute is commonly used to prosecute those who provide pornography to children.
Hogue mentioned such games as Resident Evil 4 and Grand Theft Auto.
The makers of Grand Theft Auto will distribute a new game called "Bully" in April. This game allows a person to take revenge on those who had previously picked on them.
"You can get even with bullies. You take a baseball bat and beat up their heads," Hogue said. "It is going to show kids how to respond in school. Is this what we want our kids doing?"
To violate the terms of the legislation, a violent video game would have to be "patently offensive to prevailing standards in the adult community" and lack any serious "literary, artistic, political or scientific value for minors."
Rep. Scott Wyatt, R-Logan, said such a tough standard means only the most depraved video games would fall under this bill.
But a few lawmakers, including Orem Republican Margaret Dayton and Salt Lake City Democrat Ross Romero, questioned HB257's constitutionality.
Dayton said the bill was "frustrating." She dislikes such video games but said violence has certain constitutional protections that pornography does not have.
"That's why we can have pictures in the Bible, battle scenes or war movies," she said.
Romero also didn't like the fact the bill could land a parent in jail for two weeks, if they buy an extremely violent video game for their child.
Hogue said he vetted the bill appropriately and is confident it could stand up under a court challenge.
"And it will set an example that Utah is a family state," he said.
The bill now goes to the Senate.