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McLachlan (now aligned with Japan) and Jan Lennard Struff took just 65 minutes to oust the third seeds 6-3 6-4 on Saturday.
After their superb win over the Bob and Mike Bryan in the semifinal, hopes were high that Venus and Klaasen, of South Africa, could claim their second title together as a combination, after lifting the trophy in Marseille last year.
But they were always struggling on Saturday.
Struff and McLachlan were more consistent on serve, and the German's power game, off both the backhand and forehand wings, was too hard to handle.
One particular shot stood out, with Struff anticipating a volley from Klaasen and remarkably chasing it down to bend a shot around the net and back into play.
The game was tied at 3-3 at that point, but that point gave Struff and McLachlan an opportunity to eventually break serve, and they swept the rest of the set to take it 6-3.
Venus and Klaasen lacked their usual sharpness at the net and accuracy on serve, and with such fine margins in doubles, that was enough to turn the final to their opponents.
The 2018 Wimbledon finalists rebounded in the second set, grabbing an early break, but couldn't maintain their advantage.
Venus was broken for the second time in the match to level up the set, before Klaasen found himself 0-40 down at 4-5.