Jones finished 3-for-4, Flaherty went 2-for-3 with two runs scored and Markakis had two hits and two RBI to extend his hitting streak to 14 games.
All three homers came off Jake Peavy (1-4), who was otherwise solid in a seven-inning stint in which he struck out seven with one walk.
Norris gave up a single to Brock Holt that opened the contest, then proceeded to set down 14 straight Boston batters until Daniel Nava doubled and was left stranded in the fifth inning.
The Baltimore right-hander issued a pair of walks in the sixth but prevented any damage, and capped off his stellar stint with his sixth strikeout of the night, getting Xander Bogaerts to swing and miss with David Ross stationed at third base in the eighth.
Peavy, meanwhile, shook off a first-inning homer by Jones to keep it a 1-0 game until the fifth, when Markakis followed a Flaherty single by yanking an inside curveball onto the concourse in right field.
Flaherty extended the lead to 4-0 in his next at-bat, hammering the first pitch he saw from Peavy in the seventh over the wall in right center.