The Swede holed from 17 feet on the last to cap a superb birdie-birdie-eagle finish and sign for a 66 that lifted last month's British Masters winner to 15 under alongside Frenchman Saddier.
Saddier had earlier put himself in the picture by firing eight birdies in a seven-under-par round of 65 in which the only blemish was a bogey on the second.
European Ryder Cup team member Tyrrell Hatton was their closest challenger two strokes further back after continuing his preparations for Bethpage Black by shooting eight birdies in a flawless 64, the best round of the day.
Australians Min Woo Lee and Elvis Smylie are in a group sharing 20th place on eight under after posting scores of 67 and 69 respectively.
Another player heading to New York, Viktor Hovland, was fourth on 12 under following an erratic 71, ahead of South Africa's Darren Fichardt on 11 under.
Ludvig Aberg and Matt Fitzpatrick, two more members of Luke Donald's side, were in a group of six players on 10 under.
The conditions were notably difficult for the later starters, however, and Hideki Matsuyama and Justin Rose were among those to lose ground.
Matsuyama, the overnight leader, shot a four-over 76 to fall back to 18 under and into a tie for 20th place.
Rose, who was one behind at the halfway stage, fell back to seven under after also shooting a 76 that featured five bogeys and a double.
Hovland, having also begun just one behind, had initially appeared capable of avoiding similar problems by opening with three birdies in four holes to move into the lead, but his good work was soon undone.
Successive bogeys before the turn were followed by a seven on the 12th, but he at least stabilised with a birdie at the last to sign for 71. Aberg failed to fire as he carded a 73.
Ewen Ferguson, Aaron Rai, Harry Hall (all 10 under) and Richie Ramsey (nine under) were also in contention.
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