Raheem Sterling also made his first Chelsea appearance after completing his £47.5 million move from Manchester City, but the west London side were undone by a stoppage-time penalty before losing the subsequent shootout.
The game in North Carolina was postponed for more than an hour due to an electrical storm before kick-off, but play was able to go ahead when the lightning above the Bank of America Stadium cleared.
USMNT star Pulisic opened the scoring in the 30th minute after seizing on a blocked effort from Michy Batshuayi, while Sterling showed impressive flashes after coming on at the start of the second half.
Charlotte scored all five of their penalties to earn a surprise win against Tuchel's side.
Chelsea will look to bounce back from the defeat when they face Arsenal in the Florida Cup on Saturday evening.