Andino followed by slicing a 3-2 pitch down the right field line and into the corner, allowing all three runners to score and allow the Orioles to go up 2-0 in a four-game series.
Willie Eyre (2-1) earned the victory by inducing the final two outs of the seventh inning and Jim Johnson tossed a 1-2-3 ninth for his eighth save.
Adrian Gonzalez went 3-for-5 with a two-run homer, driving in three runs in all for American League wild card-leading Red Sox.
Boston reduced its magic number to clinch a playoff spot to seven despite the setback, thanks to Tampa Bay's loss to the New York Yankees Tuesday.
Boston remains two games ahead of the Rays with seven games remaining.