Oregon blocked Zagory's 37-yard field goal attempt in the fourth quarter and it was scooped up by linebacker A.J. Tutele, who ran it back 72 yards for the score.
The game was originally scheduled for October, but the Pacific-10 Conference instituted a full round-robin conference schedule, forcing Stanford to chose between 12 straight games or the opener at Oregon.
Later, the Big Game against California was rescheduled for Dec. 2, giving the Cardinal a late bye.
Oregon had not opened against a conference opponent since 1997. Stanford opened against Washington State in 2000.
Oregon finished 10-2 last season, its best record since 2001. The Ducks were second in the Pac-10 behind Southern California with a 7-1 mark and suffered their only regular season loss to the Trojans. The Ducks lost 17-14 to Oklahoma in the Holiday Bowl.
Oregon got a big game on defense from the player replacing All-American defensive tackle Haloti Ngata.
Juco transfer Jeremy Gibbs recorded a sack, a blocked kick and caused a fumble.
The Cardinal, coming off their fourth straight losing season, are 43-26-1 in the all-time series with Oregon, but the Ducks have won the last five games, including a 44-20 victory last season.
The crowd at Autzen on Saturday numbered 58,450, a record for an opener and the fourth-biggest attendance ever.