They finished level at eight-under 134, one stroke ahead of Americans Matt Kuchar (66) and Billy Horschel (66) on a tightly-bunched leaderboard.
World number one Rory McIlroy, slowed by a double-bogey at the par-four 14th where his approach shot bounded 30 yards over the green into a hazard, fired a 69 to trail the leaders by five shots.
Day, the world number seven whose quest this year to win a first major title was ruined by a thumb injury, maintained the red-hot form he displayed last week to tie for second in the first of the PGA Tour’s four FedExCup playoff events.
“To be in contention last week and (again) this week goes to show the hard work I’ve put in the last four or five weeks is definitely paying off,” Day told reporters.
Day’s round was a tale of two halves. He was five under on the front nine but two over coming home as the swirling wind made it difficult to judge club selection.
The Australian had visions of a birdie at the par-five 18th when he had an iron in his hands for his second shot, only to drop a stroke after firing his approach over the green and taking four more shots to hole out.
“I made the front nine look very easy today (and) made the back nine look very hard, but overall I’m very happy with how I’ve played the last couple of days,” Day said.
Palmer, meanwhile, says his goal over the final two rounds was to play well enough to “make it hard on Tom Watson”.
He was referring to U.S. Ryder Cup captain Watson, who on Tuesday will announce his three wildcard selections to complete the 12-man team to take on holders Europe at Gleneagles in Scotland next month.
“I’m proud of the way I hung in today. I had to grind it out,” said Palmer. “It could have got away pretty fast (but I) stayed patient, stayed calm and salvaged even par.”
Eighty players made the cut, which fell at three-over 145, and several Americans with hopes of earning a late Ryder Cup spot bowed out early, including Brendon Todd, Kevin Na and 2012 FedExCup champion Brandt Snedeker.
The top 70 players on the FedExCup points list after the Deutsche Bank Championship advance to next week’s BMW Championship in Englewood, Colorado where the leading 30 will qualify for the Sep. 11-14 Tour Championship finale in Atlanta.
(Reporting by Mark Lamport-Stokes in Los Angeles and Andrew Both in Cary, North Carolina.; Editing by Gene Cherry/Mark Lamport-Stokes)