Thierry Henry, right, and Tim Cahill are emotionally deflated after wasting a prime opportunity to score in Thursday’s playoff matchup with D.C. United at Red Bull Arena. (Nick Laham/Getty Images)

D.C. United’s decisive playoff match against the New York Red Bulls had offered everything except goals Thursday, but with extra time looming on a riveting evening of soccer, rookie Nick DeLeon scored in the 88th minute to secure a 1-0 victory and passage to MLS’s Eastern Conference finals.

Second-seeded United won the two-game stage on a 2-1 aggregate score and will play for the conference title for the first time in six years. The series will begin Sunday afternoon in Houston against the fifth-seeded Dynamo and conclude Nov. 18 at RFK Stadium.

“It’s been a great journey,” DeLeon said. “It’s not over yet.”

DeLeon was the last of several heroes. Bill Hamid made three stellar saves before being ejected midway through the second half. His replacement, Joe Willis, stopped Kenny Cooper’s penalty kick after the New York striker’s successful attempt was nullified by a teammate’s encroachment violation.

Lewis Neal, an English midfielder, filled in at left back for an injured starter. And Robbie Russell, a veteran defender covering for a suspended teammate, supplied the pass to DeLeon in stride in the penalty area.

“I just saw a black shirt running across my face and wanted to put [the ball] in front of him,” said Russell, who had played just 12 minutes since returning from a foot injury in mid-September.

With New York’s Connor Lade keeping DeLeon onside, DeLeon calmly rifled a low shot past Luis Robles from 12 yards. It touched off celebrations on the sideline and high above the receiving net, where several hundred D.C. supporters had gathered for a second consecutive night following a snow-influenced postponement.

“This organization has been through some tough years and these fans have suffered,” Coach Ben Olsen said of a five-year postseason drought. “They were here yesterday and then today. They are probably booking tickets to Houston. I don’t think they will ever work again. Some of them are going to get fired.”

Although United was the higher seed in the series, the club was without injured star Dwayne De Rosario and faced a New York squad with big-ticket players. It also lost the slight home-field advantage when the league switched locations of the matches following Hurricane Sandy’s impact on the New York area.

“Money can’t buy character,” United President Kevin Payne said, “and this team has a lot of character.”

Hamid, who conceded an own goal in the 1-1 draw in Washington last Saturday, thwarted former United captain Dax McCarty in each half. The second was a gem in the 65th minute on a volley inside the six-yard box.

But four minutes later, Hamid was sent off for taking down the freewheeling Cooper at the edge of the penalty area.

“I had no idea Kenny Cooper wanted to go out for the Olympic trials — I think in diving,” said Hamid, who protested to both referee Mark Geiger and an assistant referee before retreating to the locker room and tweeting his displeasure. (The tweet was subsequently removed.)

Willis, a second-year pro who made 10 regular season starts this year, entered in the most difficult circumstances: to face a penalty kick. Cooper converted, but Geiger nullified it because Thierry Henry had entered the area before the shot.

On Cooper’s second attempt, Willis guessed correctly, sliding to his left to block the low shot. “You don’t have a lot of time to think when something like that happens,” said Willis, who will start Sunday for the suspended Hamid. “I was just moving as fast as I could to get out there.”

The match took another turn in the 75th minute when New York’s Rafael Marquez wiped out Chris Pontius and received his second yellow card. With teams at even strength, Pontius missed the far corner by a whisker and McCarty squandered a clear chance in the box.

Had the match remained even, the teams would have gone to 30 minutes of overtime and, if necessary, penalty kicks. But in typically improbable fashion, United continued its autumn surge.

“We’ve been doing this for a couple of months now,” defender Brandon McDonald said of a 6-0-3 streak without De Rosario. “We’ve been hearing all the doubters say D.C. United is on the way out, it’s their last game. We just keep finding a way.”

United notes: Club officials are anticipating an extended suspension for Andy Najar, who flung the ball at the referee in the first match. . . . United’s all-time playoff record against the Red Bulls is 6-1-2.

SEATTLE 1, REAL SALT LAKE 0: Mario Martinez, starting his first MLS game, scored the winning goal in the 81st minute for the visiting Sounders, who advanced to face Los Angeles in the Western Conference finals.