Heliovaara and Patten came through their First Round match unscathed on Wednesday, knocking out Brits Dan Evans and Henry Searle in straight sets.
That set up a Second Round meeting with another pair of British wildcards in Harris and Willis, and just as in their opening match, neither duo was able to force a loss of serve in the first set, therefore a tiebreak was needed.
Having defended one set point to level the tiebreak at 6-6, the British pair then lost serve in the next rally, handing Heliovaara and Patten the chance to wrap up an 8-6 tiebreak win, which they duly took.
The second set looked to be heading the same way, until the sixth game, when off the serving of Harris, the two tied at world number three broke without dropping a point to take a 4-2 lead.
They then made no mistake on their final two service games, taking match point at the first attempt to register a 7-6, 6-3 victory in one hour and 20 minutes.
In the Third Round, they will face the winners of the match between Pierre-Hugues Herbert & Jordan Thompson and Mattia Belucci and Fabian Morozsan.
Heliovaara will be back on court tomorrow, as his mixed doubles campaign with Kazakh partner Anna Danilina gets underway.