Przybylko and Federico Navarro scored three minutes apart in the first half and Gabriel "Gaga" Slonina made three saves for the Fire (8-10-6, 30 points), who improved to 4-0-1 in their last five matches.
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Yordy Reyna scored a goal in the opening minute and Karol Swiderski tallied in the 45th for Charlotte FC (9-13-2, 29 points), who have lost three of their last four games. The setback was just the fourth in 12 matches (8-4-0) for the expansion club at Bank of America Stadium.
Przybylko secured his brace after he settled a pass from Xherdan Shaqiri and deked Charlotte FC's Christian Fuchs to create some breathing room. Przybylko then sent a left-footed shot past a diving Kristijan Kahlina (five saves) for his team-leading fifth goal of the season.
Charlotte FC took advantage from the onset after they forced a turnover deep in Chicago's end of the field.
Jaylin Lindsey's cross was headed home by a diving Reyna in the opening minute. Reyna's goal was his third in his last four matches.
Chicago countered in the 21st minute after Gaston Gimenez's blast from outside of the box produced a juicy rebound. Przybylko immediately pounced on the ball and scored from a sharp angle.
The Fire claimed the lead in the 24th minute after Jairo Torres' feed was headed down by Shaqiri, allowing Navarro to unleash a left-footed shot. The ball skidded along the turf and past a diving Kahlina for Navarro's second goal of the season and first since June 29.
Chicago failed to properly clear the ball late in the first half and Swiderski made it pay, scoring from close range to forge a 2-2 tie. The goal was his team-leading seventh of the season, with all seven being scored in Charlotte.