Between that quartet, New Zealand can boast 14 four star eventing titles, Todd has nine, Tait three, Price and Johnstone one apiece.
New Zealand had been second after the dressage phase, but slipped one spot by the end of the show jumping stage before storming home to win on the back of outstanding cross country work.
New Zealand finished on 112.9 penalty points, with France second on 130.5 and Swden third on 146.3. Germany had to settle for fifth.
"We executed a team-driven plan," Price said.
"We just wanted to be consistent through all three phases. All of us Kiwis worked cohesively very, very well. I am super happy for this and excited going forward.''
Aachen is considered to be the closest event to a true championship outside of the Olympics and World Equestrian Games.