Gaven took over for goalkeeper William Hesmer in the 86th minute after Hesmer had to leave the match after a collision with Union (8-15-7) defender Danny Califf. The Crew had already used its three substitutes.
The Union's Sebastien Le Toux made it 3-1 in the 87th minute with a strike from 20 yards that went through Gavens gloves.
Gaven drew a penalty that Guillermo Barros Schelotto converted in the 15th minute then fed Emilio Renteria to make it 2-0 in the 42nd minute. Andres Mendoza added a third goal in the 79th.
Columbus finished 14-8-8 and will face Colorado in the playoffs.