UPDATE 1-Golf-Rahm, Stenson tied for halfway lead at Hero World Challenge
Swede Stenson's 66 saw him match Rahm at 10-under 134, one shot ahead of Americans Dustin Johnson and Patrick Cantlay.
Patrick Reed went from equal first to nearly last with a 77 that left him eight shots back at Albany in the Bahamas.
Rahm, who has played a heavy late-year schedule since helping Europe to victory at the Ryder Cup in September, said his game had been dialled in.
"I missed one fairway, I believe (and) that's only because they put a patch of rough in the middle of the fairway on four," the Spaniard said.
"Didn't seem like much could go wrong. If I'm hitting really solid drives and have short irons in, it's hard not to be aggressive."
Stenson, who picked up three points from three matches at the Ryder Cup in France, was not quite as flawless but still got the job done.
"Putting has been really solid these first couple of days, short game as well, a lot of good up-and-downs," he said. "A couple of wishy-washy shots, but all in all, in good shape."
Tournament host Woods shot 69 to join Reed tied for 14th in the 18-man field, though his round could have been worse had he been penalised for a double-hit while trying to get his ball out from under a bush.
The infraction was only evident in slow motion replay and under a rule introduced last year, there is no penalty unless the double-hit can be seen in real time.
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond/Peter Rutherford)
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