Columbus (6-1-2, 20 points) is two points ahead of Toronto FC and is 5-0-3 in their past eight games at Mapfre Stadium back to July 20, 2019.
The Union (4-2-3, 15 points) lost for the first time in eight games after four wins and three ties.
The Crew has allowed two goals, tying the 2010 Los Angeles Galaxy for the fewest through the first nine games.
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Zelarayan, who missed two games this season due to an ankle injury, scored his fourth goal on a hard-luck play for the Union.
He took a pass from Pedro Santos and unleashed a shot from 25 yards that changed flight off the back of Philadelphia defender Mark McKenzie, leaving goalkeeper Andre Blake (three saves) no chance to make a stop.
Zelarayan has three game-winning goals in his first MLS season.
The goal was the first for the Crew in 237 minutes.
Philadelphia pushed for the equalizer and almost found it in the 68th minute, only to have Sergio Santos sky an open look from the right side of the box.
The scoreless first half produced chances for both sides, beginning in the 11th minute when Room went to his left to spear a deflected shot by Alejandro Bedoya.
Philadelphia's Brenden Aaronson showed his shiftiness with a dribble through the defense for a low angle shot that Crew midfielder Artur chested out of play in the 26th minute.
The Union had another chance moments later off a corner kick, but McKenzie was denied as Crew midfielder Darlington Nagbe cleared the attempt of the line.
The match was played without paying fans because of COVID-19 restrictions, but there were about 250 family members and friends of the team in the stands.
Crew SC move top of Eastern Conference with win
Lucas Zelarayan's lone strike lifts Columbus Crew SC to a 1-0 win over the Philadelphia Union. Watch MLS on ESPN+.