Liverpool star Mohamed Salah sat out of the defeat, having only returned from holiday on Friday, but observed from the sideline at Bank of America Stadium alongside Sadio Mane.
Van Dijk's header was the only shot Liverpool registered before the break, as they probed without breaking through against a young Dortmund side, who named Jadon Sancho in attack, as well as fellow Englishman Denzil Boadu in midfield.
Pulisic dusted himself off to take the spot kick and made no mistake from 12 yards, with the American-born attacker putting his effort straight down the middle.
He made a mistake in Liverpool's first pre-season game to Tranmere that once again led to a goal as his confidence appears to have taken a massive hit.
And when a Dortmund break opened Liverpool up in the 89th minute, Pulisic rifled the Bundesliga side ahead, before Jacob Larsen added a third in stoppage-time.
And the goalkeeper nearly produced another costly error, racing from his line to misplace a pass to Maximilian Philipp, who screwed a 40-yard effort wide of an open net.
Liverpool: Karius (5), Clyne (6), Matip (6), Van Dijk (8), Robertson (7), Fabinho (7), Lallana (6), Jones (6), Camacho (7), Origi (6), Markovic (5).
Dortmund then sparked their comeback as they equalised with a penalty in the 66th minute.
Previewing the meeting with his former club, Klopp admitted he was a big fan of Pulisic, whom he tried to sign for Liverpool in August 2016, and the coach was equally impressed after the match.
A quiet start to the match saw the best chance of the opening stages come from 45 yards out when Liverpool goalkeeper Loris Karius was nearly guilty of another error, coming off his line to sweep up the danger but giving the ball straight to Maximilian Philipp.