The new measures would bar sales of semiautomatic weapons to people under 21 and ban large-capacity magazines.
But Republican opposition in the Senate means the bill has little chance of entering law, despite a renewed focus on gun control in the wake of a series of mass shootings in the US.
Hours before the vote, survivors of the Uvalde school shooting gave emotional testimony to lawmakers which reduced some to tears.
The primary school shooting in the Texan city claimed the lives of 21 people, including 19 young children.
One 11-year-old girl told the hearing - in pre-recorded testimony - that she had smeared her classmate's blood on herself to play dead, and graphically described the moment the gunman shot her teacher in the head.