Wolff is only the fourth woman in the last decade to get behind the wheel of an F1 car, with Williams' development driver completing 100 kilometres of Silverstone's international circuit.
In 2002 Sarah Fisher was allowed a run in a McLaren at Indianapolis, followed by Katherine Legge in a Minardi at the Vallelunga circuit near Rome three years later.
Last year De Villota tested for Lotus-Renault in an old Renault at the Paul Ricard Circuit in France prior to joining Marussia in March as test driver.
But in July, De Villota lost the sight in her right eye after being involved in an accident at Duxford Airfield whilst conducting straight-line aero testing for Marussia.
Wolff, 29 from Scotland and wife to Williams' executive director and shareholder Toto, has admitted to being inspired by De Villota, who conducted her first press conference last week since sustaining the injury which has effectively ended her motorsport career.
"She is an incredible lady. Before you even talk about her as a racing driver, you have to know she is an incredible person, an inspiration," said Wolff.
"We were in contact a couple of weeks ago and she told me to drive for the both of us now, that I would be out there representing us both.
"I had Maria's star on my helmet, it's with pride I have that, and without a doubt I was driving for the two of us."
Wolff, who has previously competed in karting, Formula Renault and Formula Three prior to moving into DTM in 2006 since when she has driven for Mercedes, took to the wheel with no nerves.
She added: "The team gave me such a brilliant feeling, a lot of confidence this morning, so I was well prepared for it.
"Never at any point was I worried about what was happening out there. Everything was under control and it was really good fun.
"I've waited a long time for this day, I've dreamed about this day for a long time, with the first lap something special.
"I've done a lot of days in the simulator so I knew what to expect, but of course it is tremendously different when you are out there and going at those speeds.
"The track was quite dry, but there were still a few damp patches which meant there were a few little moments, but it was very exciting."
As for her progression beyond today, it is a case of wait and see as Wolff said: "This was a good step forward for me to drive a Formula One car for the first time.
"But I'm not going to run before I can walk. I have to show the team I am capable, can do the job well and hopefully get more opportunities to drive the car.
"You cannot underestimate how talented are the drivers on the Formula One grid, and how on the limit they are. It's an incredible level.
"So for me the journey is just starting, my first time in the car and let's see where that takes me."