Woods has not tasted victory at Augusta National since 2005, but contended in the last two majors of 2018 and led the Open at Carnoustie with eight holes to play before finishing sixth behind playing partner Molinari.
"It's been a while since I've been in contention here, but then again the last two majors counts for something," said Woods, who finished runner-up to Brooks Koepka in the 2018 US PGA at Bellerive.
"I've been in the mix with a chance to win in the last two major championship, so that helps. And tomorrow it will be interesting to see if that wind comes up like it's forecast, 15, 20 miles an hour around this golf course is going to be testy."
Tee times for the final round have been brought forward in anticipation of thunderstorms in late afternoon, with players heading out in groups of three from both the first and 10th tees.
The final group of Molinari, Woods and Tony Finau will tee off at 0920 local time (1420 BST), with both Woods and Finau two shots off the pace after Molinari's flawless third round of 66.
"Usually the reward for playing hard and doing all the things correctly is you get a nice little sleep-in come Sunday, but that's not going to be the case," Woods added. "We've got to get up early and get after it.
"My desire hasn't changed. I'm just thankful to be able to come back here and play again. Last year was a step in the right direction and we built a season around that and then here we are.
"I always feel pressure. The day I don't feel pressure is the day I quit. I always thought that if you care about something, obviously you're going to feel pressure.
"And I've always felt it, from the first time I remember ever playing a golf tournament to now. That hasn't changed."
All times BST
From first tee:
12:30: Aaron Wise, Marc Leishman (Aus), Kim Si-woo (Kor)
12:41: Matthew Fitzpatrick (Eng), Kevin Tway, Patton Kizzire
12:52: Henrik Stenson (Swe), Hideki Matsuyama (Jpn), Cameron Smith (Aus)
13:03: Jordan Spieth, Tommy Fleetwood (Eng), Corey Conners (Can)
13:14: Jason Day (Aus), Bubba Watson, Lucas Bjerregaard (Den)
13:25: Justin Thomas, Phil Mickelson, Jon Rahm (Spa)
13:36: Adam Scott (Aus), Patrick Cantlay, Thorbjorn Olesen (Den)
13:47: Louis Oosthuizen (SA), Dustin Johnson, Rickie Fowler
13:58: Matt Kuchar, Justin Harding (SA), Xander Schauffele
14:09: Brooks Koepka (USA), Webb Simpson (USA), Ian Poulter (ENG)
14:20: Francesco Molinari (Ita), Tony Finau, Tiger Woods
From 10th tee:
12:30: Kyle Stanley, (a) Viktor Hovland (Nor), Charley Hoffman
12:41: Kevin Kisner, Bryson DeChambeau, (a) Takumi Kanaya (Jpn)
12:52: Rory McIlroy (NI), Keegan Bradley, Gary Woodland
13:03: Jimmy Walker, J.B. Holmes, Charles Howell
13:14: Kiradech Aphibarnrat (Tha), Kevin Na, (a) Alvaro Ortiz (Mex)
13:25: Patrick Reed, (a) Devon Bling, Keith Mitchell
13:36: Tyrrell Hatton, Satoshi Kodaira (Jpn), Andrew Landry
13:47: Bernhard Langer (Ger), Rafael Cabrera Bello (Spa), Eddie Pepperell (Eng)
13:58: Branden Grace (SA), Martin Kaymer (Ger), Li Haotong (Chn)
14:09: Emiliano Grillo (Arg), Zach Johnson, Billy Horschel
14:20: Trevor Immelman (SA), Alex Noren (Swe)