The former world No 1 Woods exits at Torrey Pines after finishing his first two rounds on four over, four shots adrift of the cut.
The damage was done on the opening day as a wayward back nine on the more testing South Course left him at four over and he was unable to claw any shots back on the North Course during the second round as his two birdies were cancelled out by bogeys on three and 12.
Woods has undergone two back operations since his last regular tour appearance in August 2015. After a long lay-off he finally returned to tournament play at last month’s Hero World Challenge in the Bahamas but his rustiness was evident over the opening two rounds and he will not be around for the weekend action.
“It’s frustrating not being able to have a chance to win the tournament,” he said. “Overall today was a lot better than yesterday, I hit it better, I putted well again. We fixed a few things while I was playing today which is good.
“I need more rounds under my belt and more playing time and that is what I am trying to do.”
Olympic champion Rose is having a much better time of it as he leads by one shot on eight under.
Rose, the overnight front runner, left it late to steal the lead as after two birdies were chalked off by back-to-back bogeys at 14 and 15, the Englishman sank a 10-foot birdie at the 18th to card a one-under-par 71.
That leaves him one shot clear of Canada’s Adam Hadwin and America’s Brandt Snedeker.
“I am happy with that to be honest,” Rose said. “I was going along really nicely and playing lovely and felt like I was in control but this golf course gets tough as you turn back into the breeze.
“It is really nice to finish with a birdie on 18.”
Scotland’s Martin Laird is six shots off the lead after following up his first-round 70 with a 72.
Woods will be made to feel better about his early exit by a host of other big names joining him in missing the cut.
World No 1 Jason Day, No 3 Dustin Johnson and Rickie Fowler also failed to make it beyond the opening two rounds.