England stormed into the lead with a try from Josh Lewsey just 80 seconds into the match before France converted huge amounts of pressure into a 9-5 advantage, with three penalties from Lionel Beauxis.
But Les Bleus could not close out the game. England kept their composure and worked possession deep in French territory to give Wilkinson the opportunity to win the game - and he made no mistake.
The England fly-half once again proved the hero as he landed a penalty and a drop-goal in the final six minutes to secure the victory.
"This is a fantastic day," said Vickery.
"Sometimes in sport things don't make sense and the greatest of predictions can't get it right.
"Today was one of those very, very special days when the underdog rises up and manages to get through.
"It was not a fantastic game of rugby. It was played by two teams desperate to win a game. We managed to keep ourselves together for long enough periods of time squeak it.
"It was a fantastic day for everyone involved with the team. It is difficult to single players out. It is a team performance.
"Everyone worked hard to get into a position to get the drop-goals and the penalties."
Wilkinson missed two difficult shots at goal - the touchline conversion from Lewsey's try and a 52-metre penalty - but his quality shone through in the end.
Vickery continued: "With that final kick, if you had to put your mortgage on it he would be your man. He duly stepped up to dink it over like it was a Sunday afternoon stroll.
"Jonny is a great rugby player. People just talk about his kicks but it is his all-round game and the confidence he gives the team."
France captain Raphael Ibanez acknowledged Wilkinson's prowess and talents.
The extraordinary thing about England's progress to successive World Cup finals is that just four weeks ago they shuffled out of the Stade de France having been thumped 36-0 by South Africa in the pool stages.
That night England looked anything but World Cup finalists. But through victories over Samoa and Tonga, then Australia and now France they have developed a will and determination not to be beaten.
"Sport is a very strange animal sometimes," said Vickery.
"That South Africa game was a very bitter pill to swallow for everyone involved in the team, not just the players but supporters and the coaching staff.
"It was very painful. We have just had to bounce back.
"Samoa and Tonga were knockout games. If we didn't win we were going home. It was backs against the wall, dig in and we have done that.
"We have managed to make ourselves awkward to play. It has been unbelievable. The World Cup is a magical thing.
"Three weeks ago who'd have said England would be in the final? Let us just make sure we do ourselves justice."
Head coach Brian Ashton insisted the credit for the transformation must go to Vickery and the players.
"The players have put a massive amount of work in and deserve a massive amount of credit.
"The last two weeks have been against world class opposition and in both games they have come through strongly at the end.
"Both times they were behind on the scoreboard and have shown how strong they are mentally.
"We talked about it before the game that controlling the emotions on the pitch would probably win the game. And in the last 15 minutes the players did that better than France."