DeChambeau missed three-foot birdie putts on the ninth and 15th holes.
DeChambeau, 24 signed for a bogey-free 66 to move to 14-under 202 as the Californian looks to secure a second PGA Tour victory after capturing last year's John Deere Classic.
Woods just wrapped up his penultimate round at The Memorial Tournament, which takes place at Jack Nicklaus' club outside of Columbus, Ohio. "But I hit it really good this week, so that's a positive going into Shinnecock, where ballstriking is going to be a must".
Nineteen-year-old Chilean Niemann, who had shared the top spot after day one, had a mixed third round with bogeys on the 10th, 15th and third holes cancelling out three birdies as an eagle on the seventh saw him reach two-under for the day.
The 4-foot miss for par on the final hole certainly contributed to his fiery mood. "And so I'm able to do this now at this level and go hit the shots I'm hitting and compete and I've had a chance to win a few times so far this year".
"I did not putt well today", Woods told reporters.
For Woods, the last memory of his four rounds at Muirfield Village will be sublime ballstriking, the best in the field and better than anything he has produced going back to the first of his four back surgeries.
"The scary thing is, as well as he's hitting the ball, he's not putting well", said Patrick Reed, the Masters champion who played with Woods on Saturday and shot 73. World number one Justin Thomas was two under through 12.
But at the final hole his drive hit a tree on the right side of the fairway and careered into an unpleasant lie in the thick rough on the left and he dropped a shot to close with a 70.
Stanley joined Niemann and Cantlay on 13 under ahead of Sunday's final round thanks to six birdies and four bogeys.
Henrik Stenson (66) and Justin Rose (66) were among five at 137 with Dustin Johnson (66), Bubba Watson (67) and Adam Scott (66) also in contention at 138.
Niemann, 19, from Chile, and Stanley were 11-under and tied for the lead entering the third round.
He still was in good shape to win in just his fifth start on the PGA Tour.