The duo had booked their spot in the last eight at Roland-Garros after recording their third straight-sets win of the competition on Sunday, beating Rohan Bopanna and Adam Pavlasek 6-2, 7-6.
But it was clear from early on this morning that the number nine seeds would provide a sterner test - the Americans broke Heliovaara's first service game to take a 3-1 lead, in what was the first time all tournament he and Patten had lost serve.
The Finn and Brit were forced to save break point in the next service game, before eventually staying within touching distance at 4-2, however, they never came close to breaking back before Harrison and King secured a 6-3 victory in the first set.
Heliovaara and Patten came out strongly in the second set, taking the first game without dropping a point, only for lightning to strike twice for the number two seeds, as once again they would lose serve in the third game of the set, off the serving of the Finn.
The next seven games were all won comfortably by the serving duo, thus Harrison and King took the win in the second set, sealing the victory with their one and only match point to record a 6-3, 6-4 score in the one hour match.
The world numbers 18 and 19 will either face Joe Salisbury and Neal Skupski of Great Britain, or Matthew Ebden and John Peers of Australia in the Semi-finals.