Heliovaara and Danilina were first seeds for the competition, but that status did little to help them early on as they suffered a loss of serve in the third game of the first set.
Their attempts to break back came to little, as Verbeek and Siniakova not only held serve with ease, but broke again in the seventh game before strolling to a 6-2 first-set win.
The second set was a much more even contest - both duos defended serve with ease and it always looked destined for a tiebreak.
In the deciding game, Heliovaara and Danilina finally showed their worth, winning three points against serve to win the tiebreak, 7-2, and the second set, 7-6.
However, things went downhill quickly for the Finn and Kazakh in the third set; trailing 2-1, they proceeded to lose the next three games - two off their own serve - without winning a single point.
That almost became four-in-a-row, only for them to save the first match point, but they could not prevent Verbeek and Siniakova from sealing the match at the next attempt for a 6-2, 6-7, 6-1 win.
36-year-old Heliovaara will have to put the disappointment behind him when he and Henry Patten take on France's Pierre-Hugues Herbert and Australia's Jordan Thompson in the men's doubles Third Round tomorrow.
