Lynch ran for 122 yards and a fourth-quarter touchdown, while the Seahawks' special teams unit came up with two huge plays to establish a 10-point lead in the first quarter.
Rookie Russell Wilson threw for 151 yards in his first NFL victory, directing a 90-yard scoring drive in the third quarter capped by a 22-yard touchdown strike to Anthony McCoy.
His opposite number Tony Romo completed just 23 of his 40 passes, with his 22-yard touchdown throw to Miles Austin in the second quarter the only score the Cowboys (1-1) mustered.
Seattle (1-1) took control straight away as Michael Robinson forced Felix Jones to fumble on the opening kick-off, leading to a short field goal which gave the hosts the lead.
Malcolm Smith then blocked Chris Jones' punt and Jeron Johnson returned the ball for a touchdown to give Seattle a 10-0 lead in less than five minutes.
Dallas' early special teams meltdown did not help Romo to erase the memory of his last trip to Seattle, when he famously bobbled the snap of a potential game-winning field goal in the 2006 NFC wild-card game.
The Cowboys quarterback was picked off once and nearly had two other passes intercepted as he was unable to mount a drive of longer than 45 yards in the second or third quarters.
Instead it was the Seahawks who took control after half-time, with McCoy grabbing his score to give the home side a 20-7 advantage heading into the fourth quarter.
And it was in the final period where the running ability of Lynch allowed Seattle to control the clock, the tailback capping his display with a three-yard touchdown run with 7:57 left.