Russ Smith added 14 points and six rebounds and fellow guard Peyton Siva had nine points and seven assists as the Cardinals (19-4, 7-3 Big East) won their third straight game by holding Rutgers to a season-low point total.
It was the seventh time they have held an opponent under 50 points this season.
Gorgui Deng added eight rebounds and six blocked shots as Louisville beat Rutgers for the seventh straight time and 11th in 12 meetings.
Eli Carter had 13 points and Myles Mack 12 to lead Rutgers (12-9, 3-7). The Scarlet Knights have lost five in a row and six of seven.
Louisville blew the game open in the first eight-plus minutes of the second half, taking a 21-point lead.
Wally Judge tied the game at 28 for the Scarlet Knights with a dunk on their first possession, and then it was all Louisville.
Blackshear, who twice scored 18 points this season, broke the tie with a 3-pointer and Siva quickly stretched the lead to six with another long-range shot.
Rutgers, which went 4:07 without a point, saw Blackshear add two free throws to push the lead to 36-28. Chane Behanan made it nine with a free throw and then Smith and Siva had steals in the backcourt to set up two free throws by Smith and a rebound follow by Dieng for a 41-28 advantage.
Austin Johnson ended the drought for Rutgers with an uncontested layup before Louisville scored the next 10 points. Siva started the run with a layup, Montrezl Harrell scored on an ally-oop dunk and Luke Hancock and Smith closed the run with 3-pointers for a 51-30 lead.
That was enough for Rutgers fans, who started to leave the arena with less than 12 minutes to play. Louisville led by as many as 25 in the closing minutes.
Coming off an impressive win over then-No. 25 Marquette, Blackshear scored seven straight points to help the Cardinals jump to a 12-4 lead.
Louisville never lost the lead, but it was lucky to leave the floor with a 28-26 edge after some very sloppy play.
What was surprising was that the Cardinals led despite getting only seven points from Smith and Peyton on 2 of 7 shooting.
Carter kept Rutgers in the game, scoring 11 points on 4 of 9 shooting. The rest of the team made only five other baskets in the half.