Orlando got goals from Chris Mueller in the 41st minute and Tesho Akindele in the 66th. The Lions had three losses and a draw in their previous trips to Columbus.
The Crew (5-11-2, 17 points) have five losses and a tie in their past six games and are 1-10-1 in the last 12 matches.
The Crew have been shut out seven times, including in two straight, and are 0-3-1 in the past four home games.
He now has four shutouts this season.
Akindele added the insurance marker with a blast from 25 yards for his sixth goal of the year, on Orlando's second shot of the game.
Orlando scored on its lone shot of the first half, taking the lead on Mueller's fourth goal. He scored three times as rookie last season.
Nani had a flick to Mueller at the top of the box, and he poked the ball past goalkeeper Jon Kempin. The Lions finished with just three shots, all on target.
The Crew had three dead-ball chances in stoppage time of the first half. The first came on a free kick and was saved at the goal line when defender Robin Jansson took a deflected ball off J.J. Williams in his face. Pedro Santos then had a corner kick that went off the near post, and his follow-up corner went off Williams and the right post to end the half.
The teams play again Wednesday as the Crew travel to Real Salt Lake, and Orlando hosts the Philadelphia Union.