The Red Sox got the early upper hand in their best-of-seven series with an offensive blitz that staked them to a 5-0 lead after just two innings.
Mike Napoli clubbed a three-run, bases-loaded double in the first and Jon Lester pitched seven shutout innings in front of a sold-out crowd of 38,345 at Fenway Park.
"You want to make sure you get these wins," Lester said. "You really have to bear down in these situations and play good baseball and try to get some wins in front of the home crowd."
Napoli's double to centre field in the first inning came just moments after the umpires reversed a blown call -- a change that loaded the bases for Boston.
Lester finished with eight strikeouts for the Red Sox, who will try to take a 2-0 lead in the best-of-seven series when they host game two on Thursday.
The Red Sox will hand the ball to John Lackey for Thursday's game two while the Cardinals will send rookie sensation Michael Wacha to the mound.
Lester allowed no runs on five hits in just over seven innings.
Slugger David Ortiz had a two-run homer in the seventh for Boston, who wasted little time getting on the scoreboard.
"Getting that first win out of the way is a good feeling as we continue to try and build some momentum," said Boston manager John Farrell.
Boston have won seven World Series titles, their most recent a sweep of the Colorado Rockies in 2007. The Cardinals have won 11 crowns, with their last coming just two years ago against the Texas Rangers.
Whoever wins the series will have the most championship titles (three) over the last 10 Major League Baseball seasons.
St. Louis starter Adam Wainwright lasted five innings, giving up five runs on six hits for the Cardinals who also lost veteran Carlos Beltran with rib injury.
Beltran, who was making his World Series debut, slammed into the outfield wall stealing a grand slam away from Ortiz with a brilliant catch in second inning. He left the game and was taken to hospital where he was diagnosed with a rib contusion.
"We had a wake-up call," said Cardinals manager Mike Matheny. "They are frustrated. I am sure embarrassed to a point."