After reaching the last four at Queen's Club, the top seeds for the Eastbourne Open had won their first two matches without dropping a set, but that record looked to be under real pressure when Behar and Vliegen broke serve in the seventh game.
Heliovaara and Patten could not find the quick response they needed, and their unseeded opponents closed out a 6-4 victory in the first set.
The second set followed a similar pattern for the Finn and Brit - this time, they lost serve in their third service game of the set to trail 3-2, and were making few inroads as they attempted to break back.
Trailing 3-5 and serving to stay in the match, the Wimbledon and Australian Open champions were 30-0 up before conceding four points in succession, as Behar and Vliegen secured victory with their only match point of the contest - 6-4, 6-3.
Heliovaara and Patten will be second seeds at Wimbledon, which begins on Monday.
Behar and Vliegen, meanwhile, head to the Final at Eastbourne, where they will meet Britons Julian Cash and Lloyd Glasspool.