D.C. United’s regular season has followed a troubling course, so it was only fitting that the club’s venture into the U.S. Open Cup on Tuesday turned into a surreal exercise in anguish.

Facing an opponent two tiers down in the American soccer system, United was painfully dull, unimaginative and wasteful through 120 scoreless minutes, but survived a penalty kick tiebreaker with the Richmond Kickers, 4-2, in front of 4,752 at City Stadium.

On June 12 at Maryland SoccerPlex, United will face the Philadelphia Union — a 2-1 winner over the fourth-tier Ocean City (N.J.) Nor’easters — in the fourth round of the 100th annual tournament, which features teams from all levels of the sport.

“This tournament means a lot to us right now, especially with the situation we are in in the league,” Coach Ben Olsen said of his team, which is 1-9-2 in MLS.

After hitting the frame twice in the first half and watching Chris Korb and Carlos Ruiz ejected late in overtime, United looked to goalkeeper Joe Willis in the tiebreaker. Willis, who stopped a penalty kick in the MLS playoffs last fall, thwarted the Kickers’ first two attempts.

He credited goalkeepers coach Preston Burpo, who had studied the tendencies of Richmond’s penalty takers over the years. Willis went to his left against both Sascha Gorres and Joseph Ngwenya, smothering the imprecise efforts.

“He told me [Ngwenya] likes to do a stutter-step and then [shoot] to the keeper’s left,” Willis said.

United converted all four attempts against Andrew Dykstra, who is employed by D.C. and is on loan to the Kickers this season. Dykstra practices with United all week and reports to Richmond for weekend matches in third-division USL. (The Kickers are undefeated in league play.)

“We had a little chuckle, knowing Dykstra knows our guys a little better than we knew theirs,” Olsen said. “We have a lot of faith in Joe in those situations.”

Despite starting eight regulars, United labored to capitalize on dominant possession. Richmond sat back, absorbed and aimed to counterattack (with minimal effectiveness).

“It’s not easy to break teams down that are that committed and defend with those type of numbers,” Olsen said. “Do we need to be better unlocking teams? Yes. We need to be a little bit less predictable in everything we do. Hopefully that will come.”

United failed to finish its few opportunities. Lionard Pajoy’s angled header off a corner kick crashed off the barrier. Dwayne De Rosario’s point-blank header stung the inside of the right post before hopping along the goal line without crossing it. And Conor Shanosky’s diving header from short distance missed wide.

The second half was a bore: United misdirected passes, while Richmond mustered infrequent forays. In overtime, Korb was sent off after receiving a second yellow card in the 114th minute and Ruiz left three minutes later for a harsh midfield challenge.

“We just wanted to come out and get a win any way possible,” said defender James Riley, who converted the clinching penalty kick. “The guys gutted it out and were able to make it happen. Hopefully this snowballs and gives us a bit of momentum.”

United notes: The club announced the signing of Sainey Nyassi, a Gambian winger who was released by New England two weeks ago. He entered at the start of overtime. . . . United will return to league play Sunday at Chicago.