And while the position might be unfamiliar - inside centre, rather than fly-half - Woodward expects his superstar World Cup-winner to deliver.
"Jonny is at his best in these big games," said Woodward.
"He is the player I want out there when the pressure is at its greatest, and his state (mentally and physically) is very, very strong.
"The kick against Argentina in Cardiff last month nailed any doubts about his mental state."
Wilkinson's last-gasp strike allowed the Lions to escape with a 25-25 Millennium Stadium draw before they headed to New Zealand, and he will once again have goalkicking responsibility in what is predicted to be a wet-weather encounter.
The Lions are targeting the first of two victories required to end 34 years of Test series failure in New Zealand and Woodward insisted he was comfortable with his starting line-up.
"This is a huge pressure game," he added. "We are here to win, and it is about walking off the pitch with more points than the team in black. Sport remembers winners, not losers.
"It was a difficult selection process, but I am delighted with the team I've picked. I have had to make some pretty tough calls.
"When I was in charge of England, I felt a huge amount of responsibility, and I feel even more responsibility doing this job, because you are representing four countries.
"It would have been easy to make some popular decisions (in selection), but I am not here to be popular, I am here to win a Test match."
With Christchurch painted red by an invasion of Lions fans, Woodward is relishing the atmosphere for one of rugby's most eagerly-awaited clashes since the professional era dawned.
Among the many good luck messages received at the Lions' city centre base have been support from Prime Minister Tony Blair, his Irish counterpart Bertie Ahern and Springboks coach Jake White, while Woodward revealed that coach Ian McGeechan will present the players with their Test jerseys.
McGeechan is a veteran of six Lions tours as a player and coach, and Woodward said: "Ian is the ultimate in terms of what the Lions is about. It is a big occasion, and I cannot think of anyone better."
A Lions victory would set them up for only their second Test series success over New Zealand in almost 100 years, but the history books show just three Test match wins on the South Island, compared with 12 defeats.