American Woods, the world number one, made two birdies and two bogeys on the front nine and sank a 10-foot putt on the final green to finish on two under par along with Briton Lee Westwood and Swede Henrik Stenson.
Argentina's Angel Cabrera led the field on four under after nine holes and overnight leader Zach Johnson was three under after 10, the late starters battling fresh winds and parched fairways and greens on the East Lothian links.
Woods collected birdies at the third and fifth holes but bogeys on the fourth, eighth and 11th halted his charge and the American waved his putter in frustration after wasting a birdie chance at the 12th.
He maintained his concentration, however, to par the next six holes and a fine approach shot set up a birdie on the last which he celebrated with a trademark fist pump.
"Towards the middle part of my round I lost the pace and was blowing it past the hole," Woods told reporters. "But finally got it fixed at the end.
"Just got to continue plodding along. Continue just being patient, putting the ball in the right spots and trying.
"We're not going to get a lot of opportunities out there but when I have I've been able to capitalise and hopefully I can continue doing that."
Jimenez, 49, followed his opening 68 with a level-par 71, the cigar-loving Spaniard drawing on all his experience to mix two birdies with two bogeys in a rock-steady round.
Westwood, seeking a long overdue first major championship, took advantage of a hot putter to pick up six birdies over the first 12 holes.
He briefly moved to five under but had to settle for a round of 68 after three bogeys over the closing stretch.
"I was pleased to be five-under through 12," said Westwood. "I was playing some great stuff. And it was just getting harder as the holes progressed, tougher to score, tougher to get it close.
"The finish is tough, 16, 17, 18 are playing hard. So it's like most major championships, it's a grind out there."
Pars on the closing holes were not easy to achieve as the greens, watered overnight following complaints by some players during the first round, speeded up again.
As the players struggled to cope with the conditions, the projected cut mark increased steadily throughout the day and is now predicted to come at seven over.
Former world number one Luke Donald will certainly miss it after finishing at 10 over, a round of 72 failing to repair the damage of his opening 80.
Former Open champions Paul Lawrie and David Duval, and American duo Jim Furyk and Rickie Fowler also looked like missing the weekend's action along with world number two Rory McIlroy who had slumped to 13 over par after 12 holes.
(Editing by Martyn Herman)
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