Rutgers scored the opening basket of the second half to forge a 28-28 tie, but was then outscored 23-2 over the next 8 minutes.
Blackshear went 7-of-11 from the field and scored 19 points. It was the third straight win for Louisville (19-4, 7-3 Big East Conference), which pulled within a half game of Syracuse and Marquette for the league lead.
Russ Smith added 14 points for the Cardinals.
Eli Carter had 13 points for Rutgers (12-9, 3-7), which has dropped five in a row.