Though Day also bogeyed the 11th, he broke two strokes clear of a tightly bunched leader board with a two-putt birdie at the par-five 16th before parring the last two holes to post a 15-under total of 201.
"I feel like I stayed patient to grind out a two-under par," Day told reporters after playing through several rain showers to maintain the lead he has held from the opening round.
"It's good to be back in contention. I love the feeling of being in the lead. Now I have to push forward until Sunday is done."
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Day is seeking to become just the second Australian winner at Bay Hill, after Rod Pampling in 2006, and the first wire-to-wire winner since Fred Couples in 1992.
Long-hitting Day, who won his first major title at last year's PGA Championship, has been superb on the greens all week at Bay Hill and needed just 26 putts in the third round.
Swede Henrik Stenson, who briefly led by one after sinking a 13-foot putt to eagle the par-five sixth before rain swept across the course, returned a 70 to share second place at 13-under with Americans Troy Merritt (67) and Kevin Chappell (67).
"It wasn't the best timing," Stenson told PGA Tour radio about the impact of the rain. "I had one or two chances there but it was tough conditions and it kind of killed the momentum a little bit.
"It went from a golf tournament the first six holes to a survival contest. It's tough around here. I was in four bunkers today and three of them were plugged, so you've got some tough shots for sure."
Stenson is seeking redemption for last year, when he led deep into the final round before three-putting the 15th and 16th holes.
Former U.S. Open champion Justin Rose of England (71) was tied for fifth at 11-under with American Derek Fathauer (69) while Australian Adam Scott, seeking a third straight victory, tripled-bogeyed the last for a 70 to fall nine strokes behind.
World number two Rory McIlroy mixed three birdies with three double-bogeys to card 75 and fall a distant 16 strokes off the pace.
(Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Andrew Both)
