Quinn, who started eight games with Kansas City last season, completed 5-of-8 passes for 89 yards.
Seattle starter Russell Wilson threw for 126 yards, but was intercepted twice. Aaron Rodgers threw only seven passes for the Packers without a touchdown or an interception.
It was a 3-3 game at halftime, but Seattle took the lead in the third period on a 43-yard run by Christine Michael.
Green Bay tied it 6 minutes late on a 1-yard toss from Vince Young to Jonathan Amosa.
Seattle is unbeaten in its three exhibition games. Green Bay fell to 1-2.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
Texas principal bans speaking Spanish, stirs controversy