The walked on court shortly before 7pm in the evening Paris time and got off to a flying start, breaking Dodig twice in the first set to take it 6-2 in 27 minutes.
But the Kiwi was broken early in the second set allowing Dodig and Granollers to level the match, winning the second set 6-3.
Games went with serve until the 6th game of the decider when Granollers was broken and Venus and Harrison kept their composure to close out the match for a memorable victory.
"We started off the game well, we got up and that was key. We managed to get the first two points in the game and our energy and excitement raised and the shots started to fall for us."
They saved seven of eight break points against their serve in the match which was a telling statistic. Venus and Harrison were able to convert three of their seven break point chances.
Their prize for making the last four will be a match against the 16th seeded Colombian pair of Juan Sebastian Cabal and Robert Farah for a place in the final.
They reached the Roland Garros final in 2011 but are a team that Venus and Harrison won't be overawed playing against.
"They are an established doubles team and obviously playing well so it is going to be another tough match." Venus said.
Brett Steven was the last New Zealand male to reach a Grand Slam semi-final in doubles in Paris in 1995 with American Tommy Ho.
While his ranking is expected to surge into the top 30 in the world for the first time on the back of his unprecedented success, Venus and Harrison are also in the money. They are guaranteed to share at least 132,000 Euros (NZ$208,000) between them for making the semi-finals.
The prize money will rise to 270,000 Euros (NZ$423,000) for finishing runners up and 540 thousand Euros ($850,000) should they win the title.
Venus quipped "I've had to extend the Air B&B a few times now which is a good position to be in."
The semifinal will be played on Thursday night New Zealand time with the final if they made it scheduled for Saturday night.
Venus would love the opportunity to play on one of the two big show courts Philippe Chatrier or Suzanne Lenglen, but ultimately is just thrilled to be in the semifinals of a Grand Slam and will play anywhere.
Matt Brown is at the French Open thanks to Emirates Airline