Pretty much having their way with things at the Arnold Palmer Invitational Presented by Mastercard, Stenson added a 3-under 69 to his opening 64 to get halfway home in 11-under, tied with DeChambeau (67-66).
The American and Stenson boast a two-shot advantage over Talor Gooch, who recovered from bogeys on the first two holes with a run of five birdies in seven holes.
McIlroy, 28, began the day outside the top 10 and six off the lead, but began to make his move on the front nine, turning in two-under 34 before dropping his first shot of the day at the par-4 11th.
"Over the weekend past year I was hitting driver pretty much everywhere, leaving myself wedges in".
Rose's playing partner Woods also clawed his way back into the tournament with a 69 and at seven under lurks ominously. And then his round almost got away from him on the par-5 16th when he chunked a shot from the fairway bunker, pitched some 70 feet beyond the hole and had to make an 8-footer for par. Rickie Fowler (-8) and Tiger Woods (-7) are among those in the top 10 through 54 holes.
"I'll tell you after Augusta!" he said with a grin. Rory McIlroy was slowed again, this time with a pair of bogeys to start his back nine, though he could accept a 70. On the par-5 16th, with his ball just below the fairway bunker lip, he decided against laying up, then flew his shot over trees and water to find the green, later two-putting for another birdie. "But I'm in a better position this Friday than I was last Friday, so I'll take anything I can get".
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McIlroy shot weekend rounds of 65 and 69 past year to finish in a tie for fourth, two behind victor Marc Leishman.
After curving in a 38-foot putt at the third, Woods sank a five-foot birdie putt at the par-5 fourth and, after a par save from a greenside bunker at five, sank a 15-foot putt at the sixth.
Like most of the day, Woods was unable to get a putt to drop on the 18th after a mammoth 3-wood liner off the tee that left him just 150 yards in. He at least managed to birdie the par 5s on the back, and had a tough par save on the 15th.
The disappointment was his wedge play.
When Woods picked up Sam, 10, and Charlie, 9, from school the next day, he was surprised to hear them recount his Valspar Championship performance in detail. There are multiple major winners ahead of Woods, including leader Henrik Stenson (-12).