Georgia (5-5) led only 6-0 before scoring 35 points in the second quarter against the FCS Bengals.
Georgia has scored more than 30 points in five straight games for the first time in school history.
Idaho State (1-8), suffered its eighth straight loss this season and 26th consecutive road loss, a streak that began in 2006.
Idaho State starting quarterback Russel Hill was 2 of 16 passing for 27 yards and two interceptions, including one returned 39 yards by Rambo for a touchdown in the second quarter.
Morris replaced Hill in the third quarter and was 5 of 16 passing for 85 yards with one touchdown and one interception. Cuff, a backup cornerback, picked off a pass from Morris and scored on the 30-yard return in the third quarter.
Idaho State, a Big Sky team, played its second game against a Southeastern Conference school. The Bengals lost 41-29 at Kentucky in 2005.
Carlton Thomas led Georgia with 14 carries for 64 yards. King had nine carries for 43 yards.
Murray threw touchdown passes of 3 and 46 yards to Green and 6 yards to Figgins.
Green had six catches for 103 yards. The two touchdown catches brought Green's career total to 21 as he passed Fred Gibson for second place on the school records. Terrence Edwards set the school record with 30 from 1999-2002.
Murray completed only 5 of 11 passes for 39 yards in the sluggish first quarter. Murray, a freshman who threw three interceptions and lost a fumble in last week's 34-31 overtime loss to Florida, recovered to pass for 168 yards and three touchdowns in the second period.
Georgia led 41-0 at halftime, and coach Mark Richt left his starters in the game for one series in the third quarter. Murray's 21-yard pass to Green set up a 1-yard scoring run by Chapas.
Murray completed 19 of 27 passes for 228 yards and three touchdowns.
Hutson Mason took over for Murray and completed 3 of 8 passes for 41 yards.
Blair Walsh kicked field goals of 38 and 53 yards in the first quarter. The 53-yarder matched Walsh's career longest and left the junior 8 for 12 in his career on attempts from 50 yards or longer.
Walsh was one of three finalists last season for the Lou Groza Award given to the nation's top kicker.
Walsh's backup, Brandon Bogotay, missed a 35-yard attempt with 55 seconds remaining to end a long Georgia drive.
Freshman safety Alec Ogletree made his first start for Georgia and had a partial block of a punt late in the first quarter to help set up the Bulldogs' first touchdown drive in the second quarter.
The attendance was 92,746 for Georgia's 62nd consecutive sellout at Sanford Stadium, but there were several thousand empty seats.
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