The home runs backed a so-so start from Chris Tillman (4-7), who picked up his second straight win despite allowing four runs in 5 2/3 innings.
Wade Miley (5-6) was removed after four ineffective innings and was seen having a heated discussion with manager John Farrell in the dugout. He surrendered five runs on nine hits in the abbreviated outing.
The Orioles, winners of four straight overall, staked Tillman to a 4-0 lead.
Jones crushed a middle-in changeup into the left-field seats in the first inning, Steve Pearce singled in a run in the second, and the Orioles tacked on two more in the third.
Reimold, in his second game since coming back up from Triple-A Norfolk, smacked his first home run of the season to straightaway center, and Jones followed with a double before coming around on Delmon Young's base hit through a drawn-in infield.
A potential comeback started in the fourth when the Red Sox scratched out three runs after loading the bases with no outs. After Ortiz flew out harmlessly, Mike Napoli knocked in Dustin Pedroia with a deep fly to center.
Sandoval split the gap in left to bring two across, but Machado got one of the runs back in the bottom half with a no-doubter to left.
Tillman was pulled with two on and two outs in the sixth, and Brad Brach was greeted with an RBI single off the bat of Xander Bogaerts.
Brach struck out Mookie Betts to escape the inning and tossed a 1-2-3 seventh, and a two-base Sandoval error followed by a Matt Wieters sacrifice fly gave the hosts a much-needed insurance run.
Ortiz hammered a Chaz Roe pitch to deep right to pull Boston back within one in the eighth, but Zach Britton closed out the win with his 17th save in the ninth.