In January in Mickelson's Phoenix Open victory, he lipped out a birdie putt for 59 and settled for a first-round 60.
Woods had a 68. Masters champion Adam Scott, rounding out the 1-2-3 pairing, struggled to a 73 and joked later that he rolled out of the wrong side of the bed.
Kevin Stadler birdied his last four holes for a 64. Sergio Garcia, Hunter Mahan and Roberto Castro shot 65.
Thailand's Pornanong Phatlum birdied three of her last four holes to maintain a one-stroke lead after the second round of the Safeway Classic at Portland, Ore.
The 23-year-old Phatlum, winless in five seasons on the LPGA Tour, followed her opening 8-under 64 with a 66 for a tournament-record 14-under 130 total at rain-softened Columbia Edgewater.
Norway's Suzann Pettersen, the 2011 tournament winner at Pumpkin Ridge, was a stroke back at 13 under after a bogey-free 63. Germany's Sandra Gal was 12 under after her second straight 66, and countrywoman Caroline Masson was another stroke behind after a 64.
A 72-hole event for the time, the tournament is back at Columbia Edgewater after four years at Pumpkin Ridge. Columbia Edgewater also was the tournament site from 1990-2008.
Cristie Kerr, the winner in 2008 at Columbia-Edgewater, was 10 under along with fellow Americans Lizette Salas and Sandra Changkija. Changkija had a 66, and Kerr and Salas shot 68.
Rocco Mediate eagled two of the final four holes to take the first-round lead in the Champions Tour's inaugural Shaw Charity Classic at Calgary, Alberta.
The 50-year-old Mediate, the Allianz Championship winner in February in his first Champions Tour start, had an 8-under 63 at tree-lined Canyon Meadows. He played the final five holes in 6 under, making eagles on the par-5 15th and 18th and birdieing the par-3 14th and par-4 17th.
Bart Bryant, Jeff Sluman, Bobby Clampett and Canada's Rod Spittle were a stroke back.
Fred Couples opened with a 69.
The tournament is the 50-and-over tour's third event in Calgary. Don January won the 1983 Peter Jackson Champions at Earl Grey, and Brian Barnes won the 1998 AT&T Canada Senior Open at Glencoe.
Deutsche Bank Championship
Phil Mickelson -8
Brian Davis -8
Kevin Stadler -7
Three tied at -6
Tiger Woods -3
Daniel Summerhays -3
Rory McIlroy -1