The Blues looked to be on course for their first defeat under Mauricio Pochettino's tutelage after Marius Wolf scored late on.
Wolf volleyed home in the 80th minute from close range at Soldier Field to give the German giants an undeserved lead.
It seemed to be the winning strike with Dortmund on their way to claiming another Premier League scalp after their 3-2 win over Manchester United on Monday.
But up popped 18-year-old striker Burstow in the 89th minute to head beyond goalkeeper Alexander Meyer.
A Mykhailio Mudryk free-kick was failed to be cleared away by Dortmund, with Enzo Fernandez guiding a header back across the box.
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And Burstow, who had only been on the pitch for eight minutes after replacing Nicolas Jackson, reacted quickest to loop his effort into the far left corner.
Having made his first team debut in the 1-1 draw against Newcastle last week, Burstow has now banged in his first goal for the senior side.
It was nothing less than what the west Londoners deserved as they bossed the majority of the match.
However Pochettino, who has won three out of his five friendly matches, will be sweating over the extent of Christopher Nkunku's injury.
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The versatile French star was forced off in the 22nd minute with a knee injury.
He was later spotted with an ice pack around his left knee to spark fear he could be set for a spell on the sidelines.
Chelsea's next encounter is on August 13 when they welcome Liverpool to Stamford Bridge in the opening weekend of the new Premier League season.