At the age of 38, Hewitt still seems to be enjoying his time on the tour as a doubles specialist, but he and his Australian compatriot weren't able to live with Venus and Klaasen.
Hewitt was broken in the eighth game, with Klaasen fluking a lob on a return at break point.
Venus comfortably held serve in the next to to put him and Klaasen up a set.
Thompson was broke in the opening game of the second set, but when Klaasen attempted to serve the set out, he was broken.
In the next game Thompson hit a winner down the line on game point, however, Hewitt started celebrating before the ball had gone Venus at the baseline, so the umpire docked the Australians a point.
It was a controversial moment, but as Hewitt and Thompson went on to win that game, it didn't have any impact.
In the subsequent tiebreak Thompson and Hewitt both made unforced errors as Venus and Klaasen won it 7-3.
There was a break towards the end of the third set, which put Venus and Klaasen in the box seat and the Kiwi put away the match point with a volley at the net.
We took care of our serves really well," Venus said, reflecting on the match.
"There was one little hiccup there, but throughout a best of five set match, you're going to get into some trouble in some service games along the way.
"So we did good to bounce back after that and play a good tiebreaker and then played a good third set after that.
"So there were some really pleasing aspects, we did some things well, but there are still a couple of areas where we think we can keep improving."