"I think we had a pretty good first serve percentage also and once we are doing that and not giving away free points it makes it tough for the other guys to get a rhythm and helps us. So I am really pleased with how we played. I hadn't even won a set here in previous years so am really excited to be in the position we are now."
From the moment they broke serve in the opening game of the match Venus and Harrison never looked back despite losing the second set tie breaker.
"It was the opposite to our first round match where we got broken first and were a little tense and up tight and didn't play our normal game or style, so that helped our game and we continued from there."
They closed out the first set in 33 minutes and games went with serve throughout the second to go to a tie breaker.
Venus double faulted at 4-5 and Kubot and Melo closed out the set.
"It was the first double fault I hit all tournament, the tape and went wide, so we just re set had a joke with each other and got going again." Venus said.
The third set was even until the 5th game when Venus and Harrison broke Melo's serve and took control. They closed out the match with ease.
They will face the Indian pair of Purav Raja and Divij Sharan for a place in the quarter finals. They had ousted the 15th seed Olivier Marach and Venus's former partner Mate Pavic.
"The other guys are obviously playing well, and everyone can play, so just because we played well, it doesn't have any bearing on our next match so we just had to prepare well for it."
A win in the next match would lift Venus to the cusp of the top 30 in the world doubles rankings.
For Venus and Harrison, they are guaranteed to share 39 thousand Euros ($61,000) for making the third round and a win in their next match would see them split 72 thousand Euros. ($113,000)
This is the last tournament Venus and Harrison will play together in the foreseeable future with Harrison skipping the doubles at Wimbledon because it's the best of five sets. The American is ranked 42 in singles.
Matt Brown is in Paris thanks to Emirates Airline.