Bradley, whose last top-10 finish came at the 2000 Michelob Championship at Kingsmill, 64 tournaments ago, matched Day (70) at 12-under 204 -- four shots clear on the tropical, 7,526-yard Trump International course.
"Frankly, you're aiming 30, 40, 50 feet left of really where you want the ball to go," the 42-year-old Bradley said. "You've got to hit it on that line and just trust that the wind's going to take it.
"It's been a while since I've been in this position, especially on a Sunday. So [there are] a lot of emotions that I have to handle, plus the conditions of the golf course, and the wind and whatnot."
The 21-year-old Day hit into the water off the tee on the par-4 17th but rallied to save par with a 12-foot putt.
"The 17th was a poor decision off the tee," Day said. "I should have taken a 3-iron instead of a 3-wood, and I tried to be a little more aggressive, and instead I hit it right in the water."
He has putted well on the windy coastal course between the Atlantic and mist-shrouded mountains.
"My putting saved me so much today," Day said. "I hit a lot of chip shots to 10, 12 feet and holed them, so I was very happy with the speed. My putts were great, and the lines that I was reading was really good, too.
"I've just got to make sure tomorrow that I do the exact same as I've done the last three days. I don't want to try and be too aggressive out there. I just want to play my game and take it one shot at a time, but I've certainly played well to be in the position I am today."
Bradley praised the young Australian.
"If I can't win, I would love to see him win this golf tournament," Bradley said.
Matt Jones, tied for the second-round lead with Day after matching the course record with a 64, shot a 79 to drop into a tie for 37th at 3 under. The Australian had two double bogeys, eight bogeys and three birdies.
The $3.5 million tournament is being held opposite the World Golf Championship at Doral, which has attracted the best players from around the world.