Rossi made it 2-0 on a penalty kick at 39 minutes following a foul by Liel Abada.
Wilfried Zaha put Charlotte (6-4-1) on the board with a penalty kick in the second minute of extra time in the first half shaving the deficit to a goal.
Aziel Jackson made it a two-goal advantage again with a shot from the center of the box with a right boot at the 51st.
Abada atoned for his earlier foul scoring at the 64th from the right side of the box to get Charlotte within 3-2.
Jacen Russell-Rowe's header at the 81st put the Crew back up a pair to end the scoring.
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AP soccer: https://apnews.com/soccer