Avisail Garcia and Alex Avila hit consecutive homers during a four-run fifth and Tyler Saladino added a two-run shot in the seventh, all off struggling reliever Vidal Nuno.
Abreu extended his hitting streak to 10 games and his on-base streak to 23 with a solo shot during a two-run first against Ariel Miranda (1-1).
The left-handed Miranda pitched four innings, allowing three runs and five hits while throwing just 47 of 90 pitches for strikes.
Quintana (11-9) allowed a run and five hits, struck out eight and lowered his ERA to 2.77 in Chicago's fifth win in seven games.