With runners at the corners and two outs, Adam Jones hit a grounder to Scutaro, whose throw to second on an attempted force-out sailed past Jed Lowrie and down the right field line, allowing Brian Roberts and Luke Scott to score to make it 3-0 Baltimore.
Scott and Felix Pie homered in the eighth inning and the O's took the first of a three-game series against Red Sox at Camden Yards.
Brian Matusz (7-12) limited Boston to two runs on six hits over six frames, walking one and striking out six.
Josh Beckett (4-4) allowed two earned runs in on seven hits in seven innings of work for the Red Sox, who fell to eight games out of first in the American League East.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys