Goals from Jacob Peterson and Claudio Bieler topped-and-tailed Sporting's 2-0 victory at home as they moved to 14 points to sit just ahead of New England Revolution and New York Red Bulls in the East.
Columbus arrived in Kansas City having not won since March and fell behind early when Peterson pounced on a loose ball in the box, while Bieler capped off the hosts' triumph with a goal deep in second-half stoppage time.
To add to the Crew's woes, they finished the match with 10 players after Wil Trapp was sent off in the 81st minute.
Columbus started the MLS season brilliantly with three straight wins but their five-game run without a victory has seen them fall from the top of the Eastern Conference table to fourth, two points adrift of Sporting, New England and the Red Bulls.
Sporting hit the front in the 10th minute when Peterson pounced on Paulo Nagamura's blocked shot and crunched it past Columbus goalkeeper Steve Clark.
Columbus edged the goalscoring chances after the home side took the lead but their hopes of securing at least a draw were shattered when Trapp slid into Benny Feilhaber from behind to receive his second yellow card with nine minutes left.
In the fifth minute of stoppage time, poor control from Crew defender Michael Parkhurst allowed Soony Saad to get a foot in and the ball fell to Graham Zusi, who exquisitely chipped a pass over Clark to Bieler for a tap in from the edge of the six-yard box.
Kansas City moved ahead of New England on goal difference, while the Red Bulls, who defeated FC Dallas 1-0 on Sunday, sit third due to having one less win than Sporting and the Revolution.
In Texas, Dallas saw Je-Vaughn Watson red-carded in just the 10th minute for a high stamp on Tim Cahill.
Just before the hour-mark, Cahill was in trouble himself, as he dragged down Danny Garcia in the penalty area, but Dallas striker Blas Perez blasted his spot-kick over the bar.
The Red Bulls made the home team pay with 19 minutes left with captain Thierry Henry teeing up Bradley Wright-Phillips for the only goal of the game.
The goal was Wright-Phillips' fifth in three matches as the Red Bulls stretched their unbeaten run to four games, while Dallas suffered their second defeat in a row.
