Veteto scored on a layup to put Sacramento State (8-6, 3-3 Big Sky) ahead at 39-37 with 13:32 left in the game.
The score stayed close after that, and a bucket by Venky Jois put Eastern Washington (4-12, 2-4) ahead 53-52 with 2:23 left.
A pair of free throws by Veteto with 1:47 put Sacramento State in front to stay.
NCAA title game hero Kris Jenkins said he will withdraw his name from the NBA draft and return to Villanova for his senior season.
Andy Katz breaks down the likelihood of Villanova, Syracuse, North Carolina or Oklahoma making a run to the Final Four next season.
Florida State has announced that Xavier Rathan-Mayes will return to the court for his junior season. The 6-foot-4 guard declared for the NBA draft last month but did not hire an agent.