The second seeds saw off another British duo, Dan Evans and Henry Searle, in the opening round (7-6, 6-1), but had a much tougher start today, losing their first two service games to eventually find themselves 4-0 down.
They were able to add some respectability to the scoreboard, but Stevenson and Willis strolled to a 6-2 first-set win.
Up against it in the second set, Heliovaara and Patten knew they had to come out firing in the second set, and they were rewarded in the fourth game, securing break point to go 3-1 ahead.
The Finn and Brit barely dropped a point off their serve in the set, and they had done more than enough for a comfortable 6-3 win.
That took the match to a 10-point tiebreak, which the French Open Quarter-finalists began well by breaking serve, but the British pair broke back soon after for 2-1. The next eight points all went with serve, before another break from Heliovaara and Patten put them in the driving seat.
6-9 down, Evans and Searle had to save three match points, only for them to lose the first of those, as Heliovaara and Patten wrapped up a 2-6, 6-3, 10-6 victory.
More local opponents, Julian Cash and Lloyd Glasspool, await the world numbers three and four in the Semi-finals.