The trio thrashed around the course at the picturesque Moll de la Fusta harbour in 52 minutes and 54.9 seconds, more than a minute quicker than Spyridon Gianniotis, Antonios Fokaidis and Kalliopi Araouzou of Greece who finished second in 54:03.3.
Brazil's Allan Do Carmo, Samuel De Bona and Poliana Okimoto, gearing up for a run at an Olympic medal in home waters in Rio de Janeiro in 2016, came in third in 54:03.5.
"Our coaches were signaling to us from outside that we were on a fast pace," Lurz told reporters.
"It really was a perfect race," added the 33-year-old. "I think our goal was maybe to win a medal but to win the gold medal was absolutely unexpected. I was shocked."
The three-person teams for the event must be mixed and are typically made up of two men and one woman.
Teams start at one-minute intervals and the key to the race is for swimmers to work together to help the weakest member achieve the fastest possible time.
By ploughing a furrow through the water just in front of a team mate, swimmers can ease their passage, a strategy similar to that used by professional cyclists.
Harle said the vocal presence of many of the German swimming team at the course, which snakes around the harbour at the end of the Rambla tourist drag, had helped.
"For me the only job I had to do was to follow Thomas and Christian," she said. "It was really nice to see our entire team on the course here to support us."