Hazard and fellow summer signing Marko Marin both got their names on the scoresheet in an action-packed opening period on the west coast of America, during which Romelu Lukaku also netted twice.
Seattle were kept in it thanks to a brace from Fredy Montero but with no further goals added after the break - largely due to the inevitable wholesale changes to personnel in the second half - Chelsea ran out comfortable winners.
With the European champions missing the likes of Fernando Torres, Raul Meireles, Florent Malouda, John Terry, Ashley Cole, Daniel Sturridge, Ryan Bertrand and Juan Mata - the latter three due to Olympic duties - Roberto Di Matteo's hand was somewhat forced in terms of team selection.
The result was Hilario in goal, a makeshift defence - led by skipper-for-the-day Branislav Ivanovic- and a forward line spearheaded by Lukaku. But it also allowed a first glimpse of the club's two big summer signings in Chelsea shirts, as Hazard and Marin lined up alongside Yossi Benayoun, in behind Lukaku.
Hazard in particular was impressive, his neat touches and sharp turns causing all sorts of problems for the MLS side, who are in the middle of their domestic season and lie third in their Western Conference.
The £35 million signing from Lille arrived at Stamford Bridge amid much fanfare - some created by the player himself - but he did much to justify the hype with a debut performance which bristled with promise ahead of the new season.
The Belgian international was the stand-out player during a highly entertaining first half that boasted six goals courtesy of some excellent finishing, but also featured some woeful defending.
It was Lukaku who opened the scoring with a tidy finish after he managed to hold off his defender with a muscular run in on goal following good work in the middle of the park by Josh McEachran. The pace, power and upper body strength displayed by the young Belgian as he bore down on goal was rather reminiscent of a certain Didier Drogba, now departed for a new life in China.
Lukaku, still just 19, grabbed a second late on in the opening period to make the score 4-2, rounding the keeper and slotting home to cap an impressive first-half display.
In between those goals, Hazard marked his first appearance for Chelsea with a strike of his own, although his effort was far from spectacular, his shot taking a hefty deflection off Jhon Kennedy Hurtado before bouncing into the back of the net.
Credit to Seattle, they responded quickly to going two down, pulling one back in the 14th minute through Montero after McEachran undid his earlier good work with a sloppy pass out of defence which went straight to the Colombian.
Montero restored parity on 33 minutes with another fine finish from the edge of the box before Chelsea edged ahead again through Marin, signed from Werder Bremen this summer. The German, not wanting to be outdone by fellow new arrival Hazard, scored in similar circumstances as his strike on goal deflected past keeper Bryan Meredith.
Lukaku's second, a minute before half-time, proved to be the last of the game as Di Matteo took the opportunity to cast his eye over a number of fringe players after the break.
Fittingly for a match played in the city that gave the world grunge and Nirvana, there was plenty of teen spirit on display with the likes of Jamal Blackman, Lucas Piazon, Todd Kane and George Saville joining fellow teenagers Lukaku, McEachran and Nathanial Chalobah in seeing some action.
But the youngsters' introductions alongside the appearance of the more established Frank Lampard, Ramires, Michael Essien and Gary Cahill - as well as the myriad changes from Seattle - seemed to break up the rhythm of the game and the second half petered out without major incident.
A third new signing, Kevin De Bruyne, showed glimpses of his capabilities following his half-time introduction though, and Di Matteo cannot have had too many complaints after what was a satisfactory outing from his side.
Chelsea continue their tour of North America with games against Paris St Germain in the first football match to be played at the new Yankee Stadium in New York, the MLS All-Stars in Philadelphia and finally AC Milan in Miami.
The Blues open their Premier League campaign with an away match at Wigan on August 19.