While Woods quit at six over par, McDowell put a miserable spell behind him by moving into a share of fifth place at golf's richest event.
A month away from his US Open Championship defence, the Northern Irishman had missed three of his four previous cuts, but produced a wonderful eagle at the 16th and then a luckier holed bunker shot at the sixth to finish the opening round at Sawgrass three behind Nick Watney.
The American, who won his first World Golf Championships title in Miami in March, set the pace with a remarkable eight under 64 which included an eagle on the second - he made it from a bunker there - nine birdies, a bogey and a double bogey.
That was only one outside the course record, but Watney was just one in front of last week's winner Lucas Glover and two ahead of David Toms and also 54 year old Mark O'Meara in a real blast from the past.
Another going well after a 67 was German Martin Kaymer, who has the chance to regain the World Number One spot from the absent Lee Westwood with a top-two finish this weekend.
Kaymer was paired with Woods and said: "I was more focused on my game to see if he was in pain, but we can just hope he gets well soon."
As for his own seven-birdie, two-bogey display, Kaymer added: "I played so much more solid than I did last week when I had to think about every single shot. Today I just played and let it go."
Kaymer and McDowell were joined by Swede Fredrik Jacobson and South Africa's Rory Sabbatini.
Londoner Brian Davis led when he stood five under after 11, but bogeys followed on the 14th and famous short 17th and he had to be content with a 69.
Luke Donald, another with an opportunity to go to the top of the Official World Golf Ranking, matched that score and did not have a bogey on his card as his fine season continued.
Justin Rose was on the same mark until he bogeyed the last, while Ian Poulter also shot 70, Paul Casey and Phil Mickelson 71 and Padraig Harrington and Ross Fisher 73.
McDowell said: "I had a great weekend on the range with Pete Cowen and felt the light switch go on.
"This is the start of a really good summer hopefully, I am hoping I can get the game primed and ready."