Tiger missed the fairway at No. 15 and made bogey
He shot 30 on his front nine with four birdies and no bogeys.
He followed that up with eight pars and one bogey on the back for a 37.
He trails the leader, Adam Scott, by three shots.
Scott played nearly flawless golf, posting a first-round 64, and is the early leader in the 141st Open Championship.
There was no wind or rain for the morning rounds at Royal Lytham, and the players took full advantage of the benign conditions and soft, wet fairways to post low scores.
The early leaderboard includes some very familiar names: Paul Lawrie, Zach Johnson, Graeme McDowell, Bubba Watson and Ernie Els.
Tiger stuck to his game plan, played conservatively and is in good position heading to the second round.
Royal Lytham puts a premium on playing from the fairways. With over 205 bunkers scattered about the course, it is extremely important to be able to put your golf ball exactly where you want it.
On many tees, Tiger hit fairway wood or long iron to position his ball in the fairway, and he found 13 of 14 fairways.
No. 15 would be the only fairway he would miss all day, and it cost him his only dropped shot of the round.
He pulled his tee shot left on No. 15 into the deep, lush rough and was barely able to advance the ball 100 yards.
He still found himself in the heavy rough with 120 yards left to the green for his third shot on the par-four.
Tiger was able to hit a magnificent shot from the deep stuff and gave himself a chance to save par.
He just missed his 30-foot par save and collected his first bogey.
Tiger had a great ball-striking round that was relatively stress-free. He had many chances for birdie but was not able to get the putts to fall.
There are some big names with afternoon tee times: Phil Mickelson, Keegan Bradley, Rickie Fowler, Rory McIlroy and Padraig Harrington.
The wind and weather can change on the Northwestern coast of England in a heartbeat.
Will the afternoon wave have low wind and no rain like the morning rounds?