The Union own a 7-13-4 record (25 points) with 10 games remaining. They are 16 points behind D.C. United and the Chicago Fire, who are tied for fourth place in the Eastern Conference with 41 points. The top five teams in the conference will earn postseason berths.
Columbus, very much in the playoff hunt, improved to 11-8-6 for 39 points.
Crew forward Justin Meram drew Union keeper Zac MacMath out of the goal and then passed to an open Gaven, who tapped it in from the far post, extending his team-leading goal total to seven.
Up to that point, the Union had been dominating after gaining a man advantage when Crew defender Josh Williams earned a red card for fighting. Williams got into a brief scuffle with Antoine Hoppenot in the 69th minute. For his part, Hoppenot was given a yellow card.
"You can look at the video," Hoppenot said of the scuffle. "I don't want to talk about it."
The Union put constant pressure on the Crew with the man advantage, but couldn't finish, sort of the story of this season.
"To be up a man in the final 20 minutes and not get a result is mind boggling," Hackworth said.
The Union opened the scoring in the 29th minute when defender Carlos Valdes scored on a free kick. His 25-yard shot deflected off the wall and into the goal for his second score of the season.
"We work on those free kicks a lot in practice, and I feel blessed to score," Valdes said.
Columbus keeper Matt Lampson made his first start of the year in place of Andy Gruenebaum, who had started the previous 24 games but hurt his back during last week's 4-3 win over New England.
The Crew tied the score when Williams headed in Federico Higuain's free kick in the 41st minute. It was his first MLS goal and continued the Union's struggles in defending balls in the air inside the box.
Valdes, who injured his hamstring late in the first half, tried to go in the second half but was replaced by Ray Gaddis in the 54th minute.
Hoping to capitalize on the man advantage, the Union brought in Freddy Adu, their top one-on-one player, in the 77th minute, replacing Jack McInerney. He helped to create pressure.
In the 80th minute, Lampson made a diving save on Michael Farfan's blast. Adu's half-volley near the top of the box went wide in stoppage time as the Union continued to pepper the goal with no success.
Notes. Carli Lloyd of Delran, who scored both goals in the United States' 2-1 over Japan for the women's Olympic gold medal, received a warm ovation before the game. . . . The Union will play Saturday at New England.
Contact Marc Narducci at 856-779-3225 or email@example.com, or follow on Twitter @sjnard.