D.C. United's Josh Wolff scores the tying score in the first half against Philadelphia in a U.S. Open Cup match at the Maryland SoccerPlex. (Richard A. Lipski/FOR THE WASHINGTON POST)

U.S. Open Cup qualifiers aren’t supposed to stir such high drama: a red card, a coach’s ejection, goals by each team in overtime and, ultimately, a penalty kick tiebreaker.

D.C. United survived a tense evening at Maryland SoccerPlex on Wednesday, defeating the Philadelphia Union on penalties after a 2-2 draw through 120 minutes.

Goalkeeper Bill Hamid, making his 2011 debut, stopped one attempt, the Union missed another, and United converted all of its efforts to prevail, 4-2.

Philadelphia’s Carlos Ruiz and United’s Josh Wolff traded first half goals, and after Daniel Woolard provided D.C. with the lead in the 111th minute, former United midfielder Brian Carroll scored a dramatic equalizer seven minutes later.

The Union played a man down for the last 34 minutes after Carlos Valdes was sent off. Philadelphia Coach Peter Nowak, United’s former boss, was dismissed after Carroll’s goal for persistent dissent.

“I’m obviously glad we won, but we’ve got to win that game outright,” United Coach Ben Olsen said. “We’ve got to be a little bit savvier in how we deal with games and manage games. Up a man, we get that second goal, it shouldn’t be an issue anymore.”

The Open Cup, featuring teams from various levels of American soccer, runs concurrent to the MLS season. Only eight teams received automatic berths in the tournament proper, leaving others to navigate a convoluted qualifying system.

In the second of three qualifiers, United will host the New England Revolution on April 26 at the SoccerPlex.

With the Open Cup lacking the weight of a league game — and tucked between regular season encounters against top Western Conference clubs — Olsen started a mix of regulars and reserves.

Hamid, defenders Ethan White and Brandon Barklage and midfielder Stephen King made their debuts. Veteran midfielder Fred was the most unlikely starter, however. Earlier in the day, his wife gave birth to their second child.

The Union was more composed in the early stages, and in the 19th minute, seized on United’s sloppy defending to take the lead. From near the corner flag, Sheanon Williams delivered a long throw that skipped through the penalty area. Ruiz, one of MLS’s most prolific scorers, was given the time to settle the ball and smash a 12-yard shot past Hamid.

United lost center back Rodrigo Brasesco to a groin injury late in the half, prompting Dejan Jakovic’s entrance.

In the 45th minute, Wolff scored the equalizer off a scramble deep in the box. Branko Boskovic delivered a dangerous corner kick. White’s volley attempt was blocked. Another touch sent it to the corner of the six-yard box, where Joseph Ngwenya knocked the ball to the far side for Wolff to place a five-yard header into the near corner.

The match grew in intensity and urgency. White stabbed Boskovic’s free kick narrowly wide, Andy Najar fired a low bid wide and Faryd Mondragon made a fine save on Boskovic’s distant effort. Hamid answered with a reflex save on Danny Mwanga’s low drive.

With a man advantage in extra time, United dominated possession. Blake Brettschneider’s low shot struck the far post and Mondragon thwarted Ngwenya’s bid. After two shots were deflected in the box, Woolard, a defender, smashed a 10-yarder into the top of the net.

But with time running out, Carroll lashed a low shot that skimmed off Hamid’s hand and deflected off Woolard’s leg to force the tiebreaker. Philadelphia’s Jack McInerney missed in the second round and Hamid blocked Roger Torres’s shot in the next frame.

“I was a little disappointed I didn’t get the other two [penalties],” Hamid said. “I read their body language and went the right way, but I’m happy we are moving on.”