TUCSON, Ariz. -- Luke Falk passed for 514 yards and five touchdowns -- four to Gabe Marks -- as Washington State held off Arizona 45-42 on Saturday.

Washington State (5-2, 3-1 Pac-12) won its third consecutive game.

Falk, who had 335 yards at the half, completed 47 of 62 passes without an interception, picking apart an injury-plagued Arizona defense that sacked him only twice.

Falk's yardage total was the most ever against Arizona (5-3, 2-3). Falk broke the mark of 511 set by Arizona State's Ryan Kealy in 1998. Falk has 11 touchdown passes in the past two weeks.

With Washington State protecting a 38-35 lead, Cougars coach Mike Leach went for it on fourth-and-inches from the Arizona 6-yard line with about 2:45 to go. Falk converted on a sneak and then, after a delay-of-game penalty, hit Marks on a 9-yard score with 2:03 to go.

Arizona quarterback Jerrard Randall, who subbed for starter Anu Solomon in the third quarter, responded with a 20-yard touchdown pass to receiver Johnny Jackson with 44 seconds left. But Washington State recovered the onside kick and ran out the clock.

Marks caught eight passes for 97 yards. Cougars wide receiver River Cracraft had eight receptions for 102 yards.

Washington State led 38-21 in the third quarter, but Randall led Arizona back. He completed 11 of 16 passes for 137 yards and two touchdowns and ran for 105 yards on 10 carries.

Falk passed for 186 yards in the first quarter as Washington State led 14-0 on two touchdown passes to Marks, a 6-yarder and a 43-yarder on a catch-and-run screen pass.

Arizona tied the score early in the second quarter on a 1-yard run by running back Jared Baker and a 69-yard punt return from receiver Nate Phillips.

Marks' third touchdown, on a 2-yard pass, allowed Washington State to retake the lead. The Cougars recovered a fumble on the ensuing kickoff and Falk struck for his fourth touchdown pass of the half.