'I was just trying to imagine I was in Reno,' said Taylor, whose only two PGA TOUR wins came at the Reno-Tahoe Open.
Among a star-packed field of players beginning their tune-up for the Masters next month, Taylor's 67 tied for the best round of the day.
A blustery Bay Hill chewed up and spit out almost everybody else, leaving only nine of the 79 players to break par in round three.
Overnight leader Rocco Mediate and playing partner Paul Casey exemplified Saturday's string of surprising meltdowns. The duo combined to go 12 over par in their last 11 holes, hitting hazards and the long rough and missing makable putts on just about every hole during that stretch.
It left many wondering if Mediate, 44, was experiencing back problems again. He said he was not, and even smiled after earning some measure of salvation with a birdie at No. 18.
Curtis avoided too many mistakes and shot a 1-under 69 to move into second place at 6-under 204.
Vijay Singh had a quiet 67 to match Taylor and climbed from 19th place overnight into a share of third. He was joined at 5-under 205 by Ryder Cup captain Tom Lehman, who had a 69.
'As the round went along, the wind died a little bit and gave us more chances for birdies,' said Singh.
Sergio Garcia remained in the hunt despite a 71 and is tied for fifth place with Trevor Immelman (70), Jerry Kelly (70), Shaun Micheel (71) and John Rollins (72) at 4-under 206.
Tiger Woods, who won four straight Bay Hill Invitationals from 2000-2003, parred each of his last nine holes and still made up ground on the leader. He shot a 70 -- three strokes better than Friday's 73 -- to share 10th place with six other players, including Retief Goosen (70).
'At least I know I played better today,' said Woods. 'I had a chance to shoot under par, I just didn't do it.'
Woods' group is five shots back at 3-under 207. Among them are Mediate, who finished with a 76, and Casey, who had a 73. All in all, not a bad deficit considering the kind of day it was.
'I'm surprised. I thought the (leading) score would be 10 under,' Woods said.
Beyond the wind, players also had to deal with the half-foot rough Arnold Palmer had waiting for them this week. It dealt blows to everyone Saturday, eating up countless shots, especially among the early leaders.
Casey gave away strokes to the rough at Nos. 8, 12, 13 and 14, and it gobbled up shots from Mediate at Nos. 6 and 14. Mediate also found water at the 16th.
At different times during the day, Mediate held a three-shot lead and Casey owned a two-shot advantage.
The day's best shot came from the same shin-deep rough that was giving everyone fits. Woods, stuck in the high grass at the 16th, knocked his approach over a tree and within 9 feet. Still, he missed the putt and settled for par.
'On this golf course, if you miss a fairway it's almost automatic bogey,' Woods said.
Taylor had a pair of early bogeys at Nos. 3 and 4, then made the first of five birdies at No. 6 before adding back-to-back birdies to finish the front nine. He made another birdie at No. 12, then took a one-shot lead with a 10-foot birdie at 15.
He saved par from 12 feet at the 18th to retain his two-shot lead on Curtis.
Taylor has some recent history to reverse if he has any shot at winning his third tour title on Sunday. So far this season, he ranks 166th in final-round scoring with a 74.2 average.
'I'm just going to play like I've been playing the last few days and hope things go my way,' he said.
Looking ahead, Taylor offered his Ryder Cup experience as a crutch.
'That was the greatest pressure I've ever played under,' he said. 'Once you have done that, everything else is easier.'
Chris Couch (69) and Bo Van Pelt (70) share 10th place alongside Woods, Goosen, Mediate and Casey; while Chad Campbell (68), Stewart Cink (69), Bart Bryant (70) and Sean O'Hair are a shot further back at 208.