Nick Markakis and Ryan Flaherty also connected for the Orioles.
Norris (5-5) struck out six and walked three while matching the longest outing of his career. Coming in, he had given up four or more runs in four of his past five starts.
Boston has lost six of its past seven games after a season-high seven game winning streak. The Red Sox have been shut out five times this season.
Jones had three hits, including his 150th career homer. Markakis extended his hitting streak to 14 games with two hits.
Boston right-hander Jake Peavy (1-4) allowed four runs and eight hits with seven strikeouts and one walk over seven innings.