Rosales scored the equalizer in the 90th minute and assisted on Neagle's winner in stoppage time as Sounders FC became the first MLS side to win at LIVESTRONG Sporting Park.
Sounders FC head coach Sigi Schmid became the first in MLS history to reach 150 career victories. Schmid is the all-time leader in both regular season (150) and postseason (19) wins.
Sounders FC (11-5-8, 41 points) improves to 5-3-5 on the road this season and remains third in the Western Conference. Seattle has come-from-behind in its past four MLS victories and has beat Kansas City in its past five contests, including three game-winners in stoppage time.
Sporting Kansas City (7-7-9, 30 points) lost for the first time since May 21 at Seattle and remain tied third in the East.
Rosales pulled Seattle level in the 90th minute when Servando Carrasco played him into the box. Rosales avoided two challenges and sent a side-footed shot inside the far post.
Two minutes later, Rosales brought the ball up the center of the park and laid it off to Mike Fucito who found Neagle on the left side of the box. Neagle sent a low shot through the Kansas City defense to put Sounders FC ahead, 2-1.
Neagle scored his second MLS goal and co-leads the team with two game-winning goals.
Fucito's game-winning assist was his first point in MLS since scoring the winner against Kansas City on April 17, 2010.
Seattle played with a one-man advantage for the final 31 minutes after Omar Bravo was sent off in the 59th minute for a hard tackle on Pat Noonan, who entered the match just minutes earlier.
Seattle improved to 6-0-2 when finishing a man up.
Kansas City struck in the 20th minute when Matt Besler's long throw found an unmarked Kei Kamara for a header in front of goal from 6-yards.
Sounders FC had a pair of chances in the 69th minute but Kansas City goalkeeper Jimmy Nielsen made two difficult saves to keep Seattle scoreless. Fucito turned and blasted a left-footed shot from 18-yards that Nielsen denied and then Neagle collected the rebound and sent a low drive from the right side of the box the Nielsen saved with his left foot.
Kasey Keller denied Kamara earlier in the match when he tipped Kamara's headed attempt over the crossbar in the 7th minute shortly after Kansas City hit the crossbar. Keller also went down to save C.J. Sapong's low shot in the 51st minute.