No. 4-seeded West Virginia uglied up the game as only a Bob Huggins-coached team can, and it was almost enough. But the upset was denied and No. 1-seeded Gonzaga prevailed 61-58 in San Jose Thursday to move on to the NCAA men’s tourney’s Elite Eight. Saturday the Zags will play No. 11 Xavier, which upset No. 2 Arizona 73-71, for the West Region’s spot in the Final Four.

“We’ve been focused forever on Phoenix,” said coach Mark Few of the site of the championship. “We’re desperate to get there.”

It’s the third trip to the round of eight, but they have yet to win the next game.

In a game that featured just 34 field goals and a 51 personal fouls, both teams looked desperate. The Zags (35-1) took the lead for good, 60-58, with 57 seconds remaining on a three-pointer in transition by Jordan Mathews, who had been burdened by foul trouble.

West Virginia (29-8) missed a runner in the lane and fouled the Bulldogs’ Silas Melson, who made one of two free throws. Javon Carter, who led the poor-shooting Mountaineers (26.7 percent from the field, five of 23 on threes) with 21 points, was determined to tie the game, but missed two long threes. Looking for a third heave, West Virginia could not get past Gonzaga’s perimeter defense as time expired.

The Zags kept alive their 19th consecutive tourney bid despite the aggressive double-teaming and physicality of the Mountaineers, who tied the game at 30 at halftime thanks in part to foul trouble that crimped the Zags’ normally fluid offense.

The Zags also had 16 turnovers, including five from Nigel Williams-Goss, a target of West Virginia’s defense that often dogged him baseline to baseline. The Spokane school made only one of its final eight shots heading into intermission.

The West Coast Conference champs started moving the ball well in the second half and looked to be in control with a 45-37 lead. But the Mountaineers could not be shaken — nor could they shoot their way back in, missing 44 of 60 attempts. Carter missed 11 of 17, but his 14 second-half points gave West Virginia its best chance, tying at 55 inside two minutes.

Mathews, Johnathan Williams and Przemek Karnowski each had 13 points, but leading scorer Williams-Goss, a transfer from Washington, missed eight of his 10 shots and finished with 10 points.