It was the third straight game Halliday had thrown for more than 300 yards and the eighth time in his career.
The shutout was the first for the Cougars since 2003, when they blanked the Vandals, 25-0, to open the 2003 season.
Marks had a career high 11 catches for 146 yards, including a 43-yard catch for a first quarter touchdown.
Halliday also connected with Dom Williams on a 30-yard TD pass and Vince Mayle for a 20-yard TD.
Jeremiah Laufasa added a 13-yard touchdown run late in the third quarter and a 3-yard TD run in the fourth quarter.
Washington State dominated every aspect of the game and turned in an exceptional defensive performance to stop the Vandals cold, including a goal-line stand in the final minute to preserve the shutout.
Saturday was the first time since 2007 the schools - just eight miles apart - met on the football field. Washington State won that game in 2007 45-28 and were even more impressive on Saturday. Idaho has not defeated the Cougars since 2000.
The Cougars will now jump back into Pac-12 play with a major challenge facing No. 5 Stanford across the state in Seattle at CenturyLink Field.
Washington State's defense entered the night No. 1 in the country allowing just 99.7 yards per game passing. They had held USC to 193 total yards and Southern Utah to 213, the first time the Cougars held back-to-back opponents under 225 total yards since 1994.
The Cougars weren't as stingy against the Vandals. Idaho finished with 253 total yards and just 174 through the air.
Idaho QB Chad Chalich finished 17 of 23 for 167 yards.
Idaho committed eight penalties in the first half, including a false start that negated a completed fake punt on the Vandals opening possession. The penalties just added to the Vandals mistakes. Idaho quarterback Josh McCain was intercepted by Deone Bucannon in the first quarter and Buchanan recovered a fumble deep in Idaho territory in the second quarter. The interception was the first this year thrown by the Vandals. They began the weekend as one of just 16 teams in the country having not thrown a pick.
Washington State had three sacks in the first quarter and finished with five for the game. Idaho came in worst in the country giving up 20 sacks in three games, with Chalich getting taken down 17 times. The 20 sacks allowed were eight more than any other team in the country.