"Things went well," said Dempster. "My body felt good, my arm felt good. I was able to attack the strike zone for the most part. [It was a] good first day."
Cardinals starter Jamie Garcia also turned in a strong effort, scattering three hits and no runs over two innings. Garcia walked one and struck out two.
St. Louis came through with three runs on a bases-clearing double by Tony Cruz in the top of the third. Those runs were scored off Red Sox righty Clayton Mortensen, who is trying to win a spot in the bullpen.
The Red Sox, who didn't play any of their projected Opening Day regulars, produced their first burst of offense in the fifth, getting an RBI double by Ryan Lavarnway and an RBI single from Mauro Gomez.
The Cardinals erupted for a five-spot against Jose De La Torre in the sixth. Ryan Jackson belted a two-run single and Matt Adams capped the damage with a two-run homer.
Up next for the Red Sox: Lefty Franklin Morales, who is projected to start the season in the bullpen, will draw the start in Wednesday's 7:05 p.m. ET game on MLB.TV against the Orioles. Setup man Junichi Tazawa will also work an inning. Several prominent position players will make the trip to Sarasota, including Dustin Pedroia, Will Middlebrooks, Jacoby Ellsbury, Jonny Gomes and Shane Victorino.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.