Sloan booted a 30-yard field-goal as time expired that gave the Midshipmen a 24-21 victory over the Panthers.
Navy (4-3) snapped a two-game losing streak and needs just two wins to become eligible for a bowl game.
After Sloan missed the extra point against Toledo last week, the Rockets scored on their next possession to escape with a 45-44 victory. Sloan said he heard Pitt coaches make comments about that game when he was near their sideline. Nonetheless, he didn't feel any added pressure when he lined up for the game-winning kick.
"It's every kickers dream to be in this situation," Sloan said. "It's definitely what separates the good kickers from the bad kickers. I thought of it as just another kick. That's all I can do."
Navy finally got into a rhythm in the second half and put together its most impressive drive of the game to take a 14-13 lead with 14:28 left in the game.
Reserve fullback Quinton Singleton's 9-yard scoring run capped the 16-play, 91-yard scoring drive that took 8:15 off the clock. The teams traded touchdowns in the fourth quarter before Sloan kicked the game-winner.
Tom Savage completed 20 of 27 pass attempts for 203 yards and two touchdowns for Pitt (4-3).
Pittsburgh's Devin Street caught nine passes for 96 yards with a touchdown and became the school's all-time leading receiver. Street now has 186 career receptions, surpassing Latef Grim, who had 178 from 1998-2000.
Trailing 14-13 midway through the fourth quarter, Savage threw a 3-yard touchdown pass to freshman Tyler Boyd to give the Panthers a 20-14 lead. Street then caught a short pass for the 2-point conversion.
Navy responded on the ensuing possession and tied the game on a 10-play, 71-yard drive capped by a 2-yard run by quarterback Keenan Reynolds with 3:53 left in the game.
The Midshipmen then forced a 3-and-out on the Panthers' next possession and got the ball at Pitt's 49. Navy ran 11 plays to set up Sloan's game-winning kick.
"I wish these games weren't like this, but we'll take it," Navy coach Ken Niumatalolo said. "I'm super-happy for Nick Sloan. The guy took a beating last week. He's the guy who took the blame last week. It wasn't his fault. We lost as a team and today we won as a team."
Pitt opened a 3-0 lead on its first drive on a 25-yard field goal by Chris Blewitt on a 16-play, 68 yard drive that took 7:32 off the clock. After Don Pearson recovered a fumble by James Conner to open the second quarter, Navy took the lead on a pass from Reynolds that deflected off Geoffrey Whiteside and was caught by senior Marcus Thomas, who ran 58 yards for first career touchdown.
"Give Navy credit, in a 60-minute game, they found a way to win," Pitt coach Paul Chryst said. "I thought our guys' effort was nothing short of what I expected. Obviously, we did not make enough plays to win the game."
Another 44-yard field goal by Blewitt pulled Pitt to within 7-6 with 9:23 left in the half. The Panthers then took a 13-7 lead eight minutes later on a 12-yard pass from Tom Savage to Street.
The Panthers completely dominated the first half and held the edge in total plays (44-22), time of possession (22:07-7:53) and yardage (252-135).
Navy entered the game ranked sixth in the nation with 304.2 rushing yards per game, and managed 220 against the Panthers.
"I'm extremely proud of Nick," Navy linebacker Cody Peterson said. "After last week, it's tough for a kicker because you're in the limelight with that one play. By no means was it his fault because there were so many plays in that game. He came back this week with ice in his veins and made it."