Logan Pause, back, reacts after the Fire reach an MLS record with its 15th tie this season. (Jonathan Daniel/GETTY IMAGES)

On the surface, a draw against the last-place, two-win Chicago Fire shouldn’t have brought much joy to a D.C. United side that had been building late-season momentum. But given the trying circumstances — goalkeeper Bill Hamid’s injury, a feeble first half, a deficit in the second half — United was pleased to salvage a point.

Josh Wolff scored the equalizer in the 73rd minute Thursday night, providing United with a 1-1 tie in front of an announced 15,818 at Toyota Park.

“When you come back and tie a game, it always feels okay,” Coach Ben Olsen said. However, “we were lucky — very lucky — to be 0-0 at the half. The game probably could’ve been over at that point. The guys really worked hard in the second half — I’ll credit them for that — but we’ve got to put a whole 90 [minutes] together.”

United (7-6-10) wasn’t very good throughout the evening, and on the last act of the first half, Hamid strained his hamstring and didn’t return. Sebastian Grazzini scored against backup Steve Cronin in the 59th minute for the Fire (2-7-15), which set the MLS record for draws in a season.

But Wolff, a second-half substitute, collected Santino Quaranta’s pass and smashed a six-yard shot over goalkeeper Sean Johnson to extend United’s unbeaten streak on the road to seven (3-0-4).

Hamid returned from a red-card suspension to make two quality saves. But just before intermission, he strained his right hamstring on the most harmless of acts — a long ball on a set piece from United’s end.

“I was just getting it up the field to kill that last minute,” Hamid said. “It’s something I’ve never done to that part of my leg. Hopefully, it’s a couple of days and I’m all right.”

Hamid will be reevaluated Friday, but Cronin seems certain to start Sunday at Sporting Kansas City (8-7-9). Joe Willis, who made a sterling MLS debut last weekend, missed this trip with back spasms. United will summon him — or request an MLS pool goalie — to back up Cronin on Sunday.

Cronin allowed Grazzini’s goal but was otherwise stable, a marked improvement over his poor effort in relief of Hamid two weeks ago. That performance, combined with Willis’s display in training, dropped Cronin to No. 3 on the depth chart.

“It was a tough week for me,” he said. “There was a small lack of communication between the coaching staff and myself, but we got past that pretty quickly and Joe played great last week. I had a great week of training this week and felt prepared coming in tonight.”

Chicago set the pace — both in dictating terms of the match and unleashing its rapid forwards. Dominic Oduro raced into space three times, and in the 14th minute, sent an angled bid off the far post. Chicago’s speed forced United to chase the game, and consequently, limited D.C.’s ability to sustain possession.

In the 30th minute, Hamid soared to his left to thwart Marco Pappa’s bending free kick from almost 35 yards. Late in the half, Oduro was unable to settle Patrick Nyarko’s back-post feed.

Cronin’s first serious test came in the 59th minute — and Grazzini’s powerful, eight-yard volley was too much too handle.

In need of an attacking boost, Olsen removed the ineffective Charlie Davies and inserted Wolff. The payoff came 13 minutes later.

Dwayne De Rosario worked the ball out of the corner. His cross was deflected to Wolff, who touched the ball back to substitute Quaranta at the top of the box. Instead of firing from 20 yards, Quaranta calmly returned it to Wolff, who straddled the line with the final defender and ripped a rising shot off the underside of the crossbar for his fifth goal of the year and 80th of his MLS regular season career.

“It was an opportunity for [Quaranta] to shoot,” Wolff said. “Guys stepped to him, so as they stepped, he played a little ball. It was a tight angle and I just tried to hit it high and hard.”

Neither side threatened to break the deadlock in the late stages.

Said defender Perry Kitchen: “We didn’t help ourselves in the first half. But for how we played and the circumstances, we get out of here with a point, which is important.”

United notes: Midfielder Andy Najar, 18, has been invited to the Honduran national team for two friendlies: Colombia on Sept. 3 in New Jersey and Paraguay three days later in San Pedro Sula, Honduras. United is off during that stretch.