The Crew will host the winner of the Western Conference final, being played later on Saturday, between Los Angeles FC and Houston Dynamo, in the December 9 title game.
Home side Cincinnati scored twice in the first half of the Ohio derby, with goals from Brandon Vazquez and Luciano Acosta and they held that lead until 15 minutes from the end of regulation.
But an own goal from Alvas Powell and then a Diego Rossi goal in the 86th minute, forced the game into extra-time and Columbus utterly dominated from then on.
The decisive goal came five minutes from the end of extra-time when substitute Christian Ramirez slotted in from close-range.
It was an enthralling encounter from start to finish with Eastern Conference champions and regular season table toppers Cincinnati striking first.
Aaron Boupendza whipped in a cross from the left which US international Vazquez collected before swivelling and burying the ball in the far corner.
Cincinnati had finished rock bottom of the league in their first three seasons in MLS but after tasting the playoffs last year, they have been transformed this season.
They doubled their advantage on the stroke of half-time when, from an indirect free-kick, the league's Most Valuable Player, Argentine Acosta fired in off the inside of the post.
Columbus had played the better football and enjoyed the bulk of possession but trailed 2-0 at the break but French coach Wilfried Nancy resisted the temptation to make changes at the interval.
Boupendza almost killed off the Crew when he found space inside the box but his shot, heading to the far corner, was superbly saved by Crew keeper Patrick Schulte.
But the introduction by Nancy of German wing-back Julian Gressel and striker Ramirez from the bench in the 65th minute, proved to be inspired.
It was Dressel's cross from the right, with Ramirez lurking at the back post, that flew in off the unfortunate Powell to give Columbus a lifeline.
Uruguayan Diego Rossi, who had been superb throughout the game with his clever movement, headed over from a promising position in the 80th minute.
Five minutes later though, the Crew got their reward, when after a clever exchange inside the box by Ramirez and Cucho Hernandez, Rossi poked in the equalizer.
With Columbus having dominated the ball for long stretches, they were the team that had the energy in extra-time with Cincinnati looking spent.
But it was not until five minutes from the very end when Columbus got the winner, Kevin Molino floating a cross to the back post which Hernandez headed across to Ramirez to tap in.
Ramirez had got the late winner in the previous round of the playoffs against Orlando and the 32-year-old Californian was hailed as the hero again at the final whistle.
Columbus will be looking for their third MLS Cup title after triumphs in 2008 and 2020.
