Harrington, who also had six touchdown passes against Arizona State in last year's 56-55 double-overtime victory at Tempe, Ariz., was 19 for 32 for 319 yards. Howry had nine catches for 126 yards.
The victory moved Oregon (8-1) into a three-way tie for first place in the Pacific 10 Conference with Washington and Washington State, all at 5-1.
Arizona State's Delvon Flowers ran for 107 yards and three touchdowns, including a 54-yarder for the game's opening score, but the Sun Devils (4-4, 1-4) were held to only 272 total yards after that.
Arizona State quarterback Jeff Krohn was hit in the head on a first-quarter slide and did not play in the second half.
Howry's knack for consistently getting past the Sun Devils' defensive backs made him Harrington's favorite target. Howry's four touchdown receptions broke the school record of three set by seven other players, most recently Marshaun Tucker last year at Arizona State.
Harrington's performance showed that the Ducks seem to be able to generate offense however they please. Last week, Onterrio Smith ran for an Oregon-record 285 yards in a 24-17 win at Washington State.
In that game, Harrington threw just 26 times and had no touchdowns rushing or passing for the only time this season.
Smith got his first start at tailback in place of senior Maurice Morris, who did not play because of a pulled left hamstring.
Smith had 152 yards in 36 carries but was bottled up for the first three quarters.
The only other Oregon quarterback to throw for six touchdowns was Danny O'Neill against Stanford in 1994.
Arizona 38, California 24--Jason Johnson passed for a career-best 315 yards and four touchdowns as the Wildcats ended a 10-game conference losing streak with a victory over the winless Bears at Berkeley.
In a meeting of the Pac-10's bottom-dwellers, Bobby Wade caught touchdown passes of 50, 13 and 16 yards from Johnson, and Clarence Farmer ran for a career-best 165 yards and a score.
The Wildcats (4-5, 1-5) had 474 yards of total offense while rolling to Coach John Mackovic's first conference victory.
Arizona scored 38 consecutive points after going scoreless in the first quarter.
Cal's nightmare season under Coach Tom Holmoe reached another low point with a listless loss to the Pac-10's second-worst team. The Golden Bears (0-8, 0-6) made it reasonably close with three fourth-quarter touchdowns, but early penalties and an untold number of dropped passes kept Cal on pace for the school's first winless season since 1897.
Cal lost its 11th consecutive game dating to last season, but there's a flicker of hope.
The Bears' three remaining games include a trip to New Jersey to face Rutgers, which lost, 80-7, to West Virginia on Saturday.