The losing streak is the longest for coach Rick Pitino and Louisville (12-7, 3-3 Big East) since the 2005-06 season. It also prevented the Cardinals from getting their 1,600th win in school history yet again.
Jordan Theodore added 17 points and Jeff Robinson 12 as the Pirates (11-6, 2-4) won for only the second time in seven games.
Seton Hall seemed to be in control when Robinson took a pass from Theodore and scored a slam dunk for a 72-59 lead with 4:40 to go.
Louisville finally got its press working and ran off a 12-3 spurt with Preston Knowles scoring on a rebound follow and Sosa stealing the inbounds pass and scoring with 1:22 to go to cut the lead to 75-72.
Keon Lawrence had the ball in the frontcourt when Sosa intercepted a lazy pass toward the foul line. The guard took off for what appeared would be a fast break that would cut the lead to a point.
However, Lawrence hustled back and blocked the shot and Theodore eventually got the loose ball and found Hazell for a dunk all alone, a play on which he was lucky the officials didn't call a technical foul for hanging on the rim with 34.7 seconds to play.
A rebound follow by Samardo Samuels with 22.8 seconds left cut the lead to 77-74 and, after Thoedore made 1 of 2 free throws, Jerry Smith nailed a 3-pointer from the right corner with about a second to play to make it a one-point game.
Seton Hall had trouble getting the ball inbounds, but Hazell finally got it and was fouled with two tenths of a second to play. He made the second of two free throws and Smith did not get off a desperation 3-pointer before the final buzzer.
Seton Hall shot 59 percent from the field and outrebounded Louisville 17-12 in taking a 46-36 halftime lead.
Hazell and Pope led the way, combining for 25 points. Hazell had 15 points, hitting 6 of 7 from the field and 3 of 4 from long range.
Hazell's third 3-pointer came at the shot clock with Knowles in his face and it ignited a 13-5 spurt that pushed the Pirates lead to 38-27 with 4:04 left in the half. Theodore had six points in the run, also nailing a 3-pointer.