The Englishman opened his MLS account with a reflex-action header after a corner which was not successfully cleared by the Quakes defence, with Dane Richards putting it back into play for Rodgers to guide home in just the second minute.
He then followed it up in the 15th minute when Henry stole the ball off Ramiro Corrales on the right flank before providing a beautiful angular ball for Rodgers who got their just before Quakes keeper Jon Busch to stab home from close range.
The match was then wrapped up three minutes from time when Rodgers turned provider with a perfectly floated ball into the path of Henry and the former Arsenal star did the rest with a diving header to really give the home fans something to cheer about.
In other MLS matches, Uruguay international Alvaro Fernandez saved Seattle Sounders by scoring the equaliser in the injury time with a header from inside the box after Philadelphia Union hit the lead earlier through a Carlos Ruiz deflected free-kick – the match ended 1-1.
In Toronto, DC United were served by a Chris Pontius brace, with another Charlie Davies goal in between, to win 3-0 against Toronto FC who played the final 40 minutes with ten man after the sending off of Ty Harden whilst Vancouver Whitecaps and Chivas USA played out a scoreless draw.
Columbus Crew beat ten man Sporting Kansas City 1-0 thanks to a fine goal from a tight angle from Robbie Rogers, LA Galaxy held off a fast-finishing Chicago Fire with a 2-1 win at Toyota Park with Chad Barrett scoring the opener against his former club, Portland Timbers recorded their second win in a row with a 3-2 result over FC Dallas as Houston Dynamo beat New England Revolution 1-0 at home.
2011 MLS season – Week 5 scores