'Modern Family' Star -- Celebrated With Oregon Coach ... After Rose Bowl Win

"Modern Family" star Ty Burrell isn't just a HUUGE Oregon fan -- he's also personal friends with UO head coach Mark Helfrich ... and the two bro'd out moments after the Ducks won the Rose Bowl.

TMZ Sports has the footage showing Ty congratulating Mark while the victory fireworks were still going off in the background ... with Ty promising to head to Texas next week to support the team in the National Championship game.