Liverpool started well in Charlotte, stroking the ball about confidently despite the intense heat.
Goal-mouth action was at a premium in the first half, though Loris Karius almost handed Dortmund an opener as he raced off his line and shanked a clearance into the German's path, but he could only fire wide from just inside the Liverpool half.
The 'Reds' suffered a blow with just 18 minutes gone as Joel Matip limped off to be replaced by Joe Gomez, but it wasn't long until they were ahead.
A corner down the left was taken quickly for Andy Robertson and his clipped cross was perfect for Virgil van Dijk to rise unmarked and power a header beyond Marwin Hitz and into the back of the Dortmund net.