Midweek honours went to Minnesota after Ramirez and Quintero both scored in the first half at TCF Bank Stadium as the host won back-to-back matches.
The Revolution pulled a goal back via Diego Fagundez early in the second half but New England were left with just one win in six league games.
Minnesota made a dream start when Ramirez opened the scoring in the fifth minute after chipping goalkeeper Matt Turner after an errant header from Jalil Anibaba.
Quintero doubled the lead in first-half stoppage time – the former America forward weaving his way past Revolution defenders in a crowded penalty area before firing a low shot across Turner.
New England reduced the deficit courtesy of Fagundez's 52nd-minute penalty after Kelyn Rowe was bundled over by Alexi Gomez.
Minnesota is ninth in the Western Conference and three points outside of the play-off places, while New England remains fifth in the east.