Mexico's exit ended a run of seven successive last-16 appearances at the World Cup and the defeat for Saudi Arabia killed off what had looked to be a realistic chance of advancing from the group stages for the first time in 28 years.
Vega first failed to connect with a cross from winger Hirving Lozano early in the game and then sent a header narrowly wide in the 26th minute.
Japan are the only team to maintain a perfect record in the group stage and are now just one win away from securing a first medal in men's soccer since claiming bronze at the 1968 Games.