From a mathematical standpoint, there is no such thing as a must-win match in playoff-friendly MLS until the final few weeks of the eight-month season. But given D.C. United’s winless start to the campaign and the road-treacherous stretch ahead, Saturday’s affair with the Columbus Crew at Navy-Marine Corps Memorial Stadium did not leave an inch of mobility.

Anything other than victory would not stand.

United could’ve tumbled after losing Paul Arriola to a red card early in the second half, but fortified by organization and grit, D.C. made Ulises Segura’s first-minute goal stand up in a 1-0 victory before 12,369 in Annapolis.

“It’s a relief. I’m not going to lie,” Coach Ben Olsen said. “It’s been a while.”

In its final home game before Audi Field opens in July, United (1-3-2) snapped a nine-game winless streak and recorded its first shutout of the year.

“The thought creeps in of not getting a win and what’s going to happen [because] we’re going to be on the road for a while,” defender Steve Birnbaum said. “I wouldn’t say it was a must-win game but it was huge for us. It was important to boost morale of the group.”

United had failed to make the most of its other off-site home match, needing a two-goal comeback in the second half March 17 to salvage a 2-2 draw with the Houston Dynamo at Maryland SoccerPlex in Boyds.

Until the new stadium is christened, United will play eight straight away, including trips to Salt Lake City, San Jose, Los Angeles twice and Seattle.

Steve Clark, a former Columbus starter, celebrating his 32nd birthday with his first appearance of the year in place of the injured David Ousted. He made a brilliant save in the second half and saw two shots by the Crew (3-3-1) hit the frame.

Moments after the final whistle, Clark jogged toward the primary stands and waved wildly at the crowd.

In the postgame locker room, a message remained on the white board: “Happy bday Steve C”.

United had gone ahead 43 seconds into the match. Despite a hard, artificial-turf surface, the interplay was cool and concise.

Nick DeLeon supplied Luciano Acosta at the top of the penalty area for a back-heel pass to Arriola, who squared the ball to Segura for a wicked one-timer to the low far corner beyond Zack Steffen’s reach.

Only two D.C. goals had been scored faster: Chris Pontius (31 seconds) in 2012 and Jaime Moreno (40) in 1997.

“Good pass from Paul,” Segura said through an interpreter, “and I thought I could hit it first time.”

United kept up the pressure and, in the fourth minute, Frederic Brillant’s header off a corner kick curled wide of the far post. D.C. sustained its energy and focus, but the Crew began to gain traction and build possession (66 percent in the half, 69 percent overall).

Clark was bailed out by the crossbar on Pedro Santos’s curling free kick.

United’s challenge grew early in the second half when Arriola received a red card. Initially, referee Ismail Elfath showed a yellow for the winger’s dangerous tackle on Artur, but after consulting video replay, Elfath reached for the other card and left D.C. with 10 men for about 40 minutes.

“I wasn’t surprised” the officials turned to replay, Olsen said. “I was hoping they wouldn’t. When they went for it, I figured it was a good chance [Arriola] was going to go.”

Clark preserved the lead with a reflex gem on Santos’s running header from six yards. Five minutes later, the right post got in the way of Gyasi Zardes’s close-range header.

As the second half transpired, Olsen’s substitutions committed his team to play defense almost exclusively. In soccer, it’s called parking the bus. Given the nautical setting near the Naval Academy, United parked an aircraft carrier.

“The team responded in a great way,” Olsen said of playing a man down. “It simplified the game for us. We had one job at that point, and it wasn’t about going to get the second [goal]. It was about locking it up. … Everybody emptied the tank.”

United notes: Forward Darren Mattocks (concussion protocol) was not in uniform after taking a blow to the jaw Tuesday. … Chris Durkin entered at the start of the second half for defensive midfielder Junior Moreno, who was returning from a hamstring injury. … United is off until April 28 at Philadelphia.