Cincinnati went on to become 4-2 winners on penalties after a 3-3 draw that saw tensions boil over in the first half.
A Nick Hagglund own goal and a header from Daniel Rosero saw Kansas City race to a 2-0 lead in the opening stages of the match.
They appeared comfortable in the clash after such early success in front of goal, but were soon reduced to ten men.
Striker Pulido was in a tussle for the ball with Cincinnati defender Yerson Mosquera, who is on loan from Wolves.
The latter went down under the former's challenge and appeared to push him in frustration.
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However, Pulido reacted in aggressive fashion by headbutting Mosquera in the face.
Cincinnati's Alvas Powell came running over and so did captain Luciano Acosta, who shouted right in the forward's face.
Referee Daniel Quintero Huitron was also quick to rush the scene and brandished a straight red card for Pulido.
His dismissal proved costly for Kansas City as they conceded just moments later courtesy of goalkeeper John Pulskamp's own goal.
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Brandon Vazquez scored in the 56th minute for Cincinnati to make it 2-2, only for Gadi Kinda's penalty to put their opponents 3-2 up.
However, Acosta's stoppage-time equaliser from the spot meant that the result had to be decided via a penalty shootout.
Cincinnati went on to win 4-2 and gain an extra point in their Leagues Cup group, the competition in which Lionel Messi score on his Inter Miami debut.
Kansas City face Mexican side Guadalajara next Tuesday, but Pulido will not be able to face his former club due to his red card.