Stanford's running game didn't miss a beat without departed Christian McCaffrey, rolling to 287 yards while starting quarterback Keller Chryst passed for 253 yards in just over one half of work at Allianz Stadium.
Chryst, coming back from a torn ACL in the Sun Bowl, completed 14 of 25 passes with two touchdowns before giving way to Ryan Burns and K.J. Costello, who finished the scoring with a 25-yard run with 1:52 to go.
Love, a junior who averaged 7.2 yards per carry as McCaffrey's understudy, rushed only 13 times as he eclipsed his previous career high of 129 rushing yards, set last season at Notre Dame.
Scarlett's three touchdowns came in the first half as Stanford scored on its first four possessions and led 38-0 at the break. Scarlett ran nine times for 68 yards and had a 56-yard reception.
Freshman Colby Parkinson, rated the nation's top tight end recruit in the 2017 class, caught three passes for 40 yards and two touchdowns.
Rice redshirt freshman quarterback Sam Glaesmann, who beat out redshirt sophomore Jackson Tyner in camp, completed 7 of 18 passes for 69 yards and an interception. Tyner directed two possessions in the second half, but Glaesmann came back in to lead the Owls' only scoring drive, capped by Austin Walter's 23-yard run around right end with 6:19 left.
Stanford had a 656-236 edge in total yards.
Love ripped off a career-long 62-yard run on the game's first snap, followed two plays later by a 13-yard touchdown pass from Chryst to freshman tight end Colby Parkinson, who scored on his first play in college.
Stanford rolled from there, scoring on its next three possessions.
Scarlett muscled in for a 2-yard touchdown run, and Love made it 21-0, scoring on a 10-yard burst through the middle. Love topped 100 yards after five carries.
Scarlett's 29-yard run gave the Cardinal a 28-0 lead early in the second quarter.
The Cardinal had seven plays of 20 yards or longer in the first half, including a 56-yard reception by Scarlett en route to his third touchdown -- a 1-yard run -- for a 35-0 edge with 3:40 to go before halftime.
Stanford kicker Jet Toner hit a 40-yard field goal for a 38-0 lead on the final play of the first half.