"I made a lot of putts, the ball comes off faster and the greens are really slow - I had to put a little more hit in the stroke," added Woods, who is bidding to become the first player to win the Open at St Andrews on three successive occasions.
The 14-time major winner made a steady start to his bid, picking up a solitary birdie, at the second, during the first six holes.
He should have added another at the third, but his 15-footer stopped at the lip of the cup and he then missed a birdie chance on the fifth, failing to hole from three feet.
Woods then began to find his range with the new putter, sinking a 15ft birdie at the seventh before holing an 18-footer at the ninth, despite finding the light rough from the tee.
'Dr' Watson not endeared by elementary conditions
The American reached the turn in three-under 33 and then made par at the 10th and 11th before charging up the field with three birdies on the spin.
He dropped his first shot of the championship at the 17th when he put too much pace on a three-footer and then three-putted the last after he drove the green.
Woods's 67 matched his opening round score at the Open at St Andrews in 2000 - he went on to win the title that year.
Meanwhile, former champion John Daly was another player to shine in gloomy, yet near-perfect conditions on the east coast of Scotland.
Favourite trousers help confident Daly
Daly carded an opening six-under-par 66, but was left thinking about what might have been.
The flamboyant American - wearing a trademark pair of psychedelic purple and green trousers - raced to the turn in 31 with five birdies.
The 44-year-old had the course record in his sights at the turn but faded slightly towards the end of the round.
"I'm not too disappointed but I hit four putts coming in which I thought I had made. I left some out there," admitted Daly.
"This is only the seventh or eighth tournament I've been healthy to play in the last three years and I'm starting to get some confidence back in my game."
Five-time Open champion Tom Watson, who led last year's championship but lost in a four-hole play-off last year, rued not taking advantage of the conditions.
"I hit the ball well on the practice range but got off to a sluggish start," said the 60-year-old, who shot a 73.
"The Lady didn't have any clothes on today - she was there for the taking and the scores reflected that.
"We've seen St Andrews play like this before ,but probably won't for the rest of the week. We got the lucky part of the draw but unfortunately I didn't take advantage of it."
"The course is going to play tough tomorrow."
Phil Mickelson, who would take the number one spot from Tiger Woods if he wins at St Andrews, also went round in 73.
Mickelson hits the pin on the 12th
The four-time major winner, who has never won the Open, cited the change in weather as the reason for his mixed round that included a double bogey at the 13th and a birdie at the last.
"It happens over here and I think it kind of crept into my attitude starting out," said the 40-year-old American of the weather.
"When I woke up this morning, I saw that it was pristine conditions, not a breath of wind.
"Then when I went out, it started to pick up. It kind of affected my attitude a little bit."
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