Kansas City Sporting (9-3-6) has won a franchise-record eight straight home games, including all competitions.
Feilhaber opened the scoring in the fourth minute after Roger Espinoza's interception in the Impact backfield. Espinoza fed Kristian Nemeth, who crossed it back to Feilhaber for a left-footed blast into the right corner of the net.
Feilhaber then assisted Dom Dwyer in the 34th minute, splitting the Impact's central defense with a 50-yard pass from behind midfield. Dwyer chased it to the top of the 18-yard box where he curled it home.
Ignacio Piatti scored in the 59th minute for the Impact (6-8-3). The goal snapped Sporting KC's 355-minute MLS shutout streak.