Madison's winner came off a corner kick 55 seconds into the sudden-death extra period, on a ball flicked off the head of reserve freshman Tyler Gimbel to Madison's foot near the top of the 18-yard box.
His teammates mobbed him at midfield, piling on top of the highly coveted Division I recruit. His coach, Bob Peffle, yanked him up to give him a hug.
"That goal was probably the most important goal of my life," Madison said.
Double-teamed throughout the game, Madison still managed both Explorers goals, his 17th and 18th of the season.
"I've been double-teamed a lot throughout the season, so I'm getting kind of used to it," Madison said.
"Special players do special things," Peffle said.
The victory gives La Salle (18-1), the No. 2 team in the Inquirer's Southeastern Pennsylvania rankings, its sixth Catholic League soccer title (first since 2006). All six have come under Peffle, in his 25th season at the school.
The title caps a truly dominant league season in which the Explorers outscored opponents 60-1, averaging 33/4 scores a game.
La Salle led by 1-0 at halftime, Madison's header goal after Khristian Hall's over-the-back header pass being the difference.
No. 9 Father Judge (14-4-1) went from two forwards to three in the second half, successfully pushing into the typically staunch Explorers defense. Kevin Pohl's head ball goal off a corner kick in the 65th minute tied the game.
The goal was the first allowed by La Salle in league play this season and appeared to rattle the Explorers.
"There's obviously going to be some tension there," said Explorers keeper Leonardo Romero, whose streak of 12 consecutive shutouts ended.
La Salle took the tip as OT began, Madison dribbling through the Crusaders defense, almost at once earning a corner chance.
"For overtime, we had more adjustments in place, but didn't have time to activate them," Crusaders coach John Dunlop said.
The loss snapped Judge's 12-game unbeaten streak and ended its season.
The Explorers advance to Thursday's District 12 Class AAA title game, seeking their first PIAA state-tourney berth against Public League champ George Washington.
Father Judge 0 1 0 – 1
La Salle 1 0 1 – 2
Goals: LS–Darius Madison 2; FJ–Kevin Pohl.
Saves: LS–Leonardo Romero 6; FJ–Dylan Trush 10.
Contact Evan Burgos