Running back Byron Marshall was Oregon's top receiver with eight catches for 138 yards and two touchdowns for the Ducks, who have won 10 straight home openers. Freshman Royce Freeman, a five-star recruit out of Imperial, California, ran for 75 yards and two more scores.
Mariota's 62-yard touchdown pass to Dwayne Stanford on Oregon's first series of the game gave him the Ducks' career record for touchdowns with 79 (64 pass, 14 rush and one reception), surpassing Joey Harrington.
Trevor Bouma ran for a 3-yard TD and Miles Bergner kicked a pair of field goals for the Missouri Valley's Coyotes, who went 4-8 last season.
Mariota, who opted to return to Oregon after flirting with an early departure for the NFL, threw for 3,665 yards and 31 touchdowns last season with just four interceptions. Considered among the top dual-threat quarterbacks in the country, he also rushed for 715 yards and nine scores.
With his third touchdown pass on Saturday night, he tied Darron Thomas for career passing touchdowns at Oregon with 66. He completed 14 of 20 passes.
The Ducks finished 11-2 last season, capped by a victory over Texas in the Alamo Bowl. Oregon's two late-season losses, to Stanford and Arizona, came after Mariota injured his left knee, effectively taking the Ducks out of the Pac-12 championship and a bid for a national title.
Following Mariota's game-opening TD strike to Stanford, South Dakota drove into Oregon territory on its opening series and scored on Bergner's 47-yard field goal to make it 7-3.
Mariota hit Marshall with a 41-yard touchdown pass and Freeman scored on a 1-yard dive to give Oregon a 21-3 lead.
South Dakota drove as close as the Oregon 3 but settled for Bergner's 25-yard field goal to narrow it.
Midway through the second quarter, Marshall's 54-yard dash for the end zone ended with a fumble on the 1-yard line for a touchback. But the Coyotes fumbled after getting the ball, giving it back to the Ducks — and Mariota hit Marshall with a 11-yard touchdown pass.
Bouma, who led the Coyotes with 781 yards rushing as a redshirt freshman last season, ran for a 3-yard touchdown to make it 35-13 with 1:36 left in the first half. Mariota answered with 1-yard keeper to give Oregon a 41-13 lead at the break.
Oregon senior cornerback Ifo Ekpre-Olomu, who like Mariota decided to return for a final season at Oregon, left the game in the first half with what appeared to be a non-contact injury to his left foot or ankle.
Oregon rested many of its starters in the second half. Freshman Charles Nelson scored on a 50-yard punt return to give the Ducks a 48-13 lead in the third quarter.
Coyotes quarterback Kevin Earl completed 13 of 26 passes for 136 yards.
The game gave Oregon some things to work on before hosting No. 8 Michigan State next weekend. The defending Big Ten champions routed Jacksonville State 45-7 on Friday night.