New England (10-14-9) remained in seventh place in the Eastern Conference — two points back of sixth-place Montreal for the final playoff spot. Sporting KC (12-13-7) had its three-game undefeated streak snapped.
Kamara opened the scoring in the fourth minute. Agudelo drew three defenders near the left sideline and he found Kamara wide open in the middle for a breakaway goal. It was Kamara's 11th goal this season, but just his second at Gillette Stadium since being traded from the Columbus Crew in May.
New England took a 2-1 lead in the 75th minute on Kevin Ellis' own goal and Agudelo knocked home Kamara's cross 8 minutes later.
Dominic Dwyer tied it at 1 in the 49th minute for Kansas City when knocked in Ellis' glancing header with his knees.