Woods, who held a two-shot overnight advantage, posted a one-under-par 69 for a seven-under-par 203 total on another sweltering day at Southern Hills.
Woods, who won last year's US PGA at Medinah by five shots, is 12-for-12 winning major championships when entering the final round with the lead.
The world No 1 registered two birdies against one bogey as he played a solid round, content to watch his rivals slide back and struggle to stay in the hunt.
The top five players on the leaderboard all posted 69s.
Ames rolled in a 15-foot birdie putt on the difficult 18th hole to move into second place at four-under 206, one stroke better than American Woody Austin, who bogeyed the last.
Australian John Senden was in fourth place at two-under-par 208, with three-time major winner Ernie Els of South Africa next at 209 as only five players finished 54 holes under par.
Local favorite Scott Verplank, playing alongside Woods, double-bogeyed the par-four 12th as Woods made birdie, starting a plunge that put him seven shots behind after a four-over 74.
In contrast to Friday's exhilarating 63 that tied the lowest round ever shot in a major championship, Woods played a workmanlike 18 holes on Saturday.
The 31-year-old American birdied the fourth and 12th holes and recorded his only bogey at the 223-yard par-three 14th when he needed two putts after blasting out of a greenside bunker.
Completed third-round scores:
203 – Tiger Woods (US) 71, 63, 69.
206 – Stephen Ames (Canada) 68, 69, 69.
207 – Woody Austin (US) 68, 70, 69.
208 – John Senden (Australia) 69, 70, 69.
209 – Ernie Els (South Africa) 72, 68, 69.
210 – Boo Weekley (US) 76, 69, 65; Nathan Green (Australia) 75, 68, 67; K.J. Choi (South Korea) 71, 71, 68; Kevin Sutherland (US) 73, 69, 68; Arron Oberholser (US) 68, 72, 70; Adam Scott (Australia) 72, 68, 70; Scott Verplank (US) 70, 66, 74.211 – Trevor Immelman (South Africa) 75, 70, 66; Geoff Ogilvy (Australia) 69, 68, 74.
212 – Peter Hanson (Sweden) 72, 71, 69; Sean O'Hair (US) 70, 72, 70.
213 – Steve Flesch (US) 72, 73, 68; Ken Duke 73, 71, 69; Justin Rose (Britain) 70, 73, 70; Luke Donald (Britain) 72, 71, 70; Anders Hansen (Denmark) 71, 71, 71; Stuart Appleby (Australia) 73, 68, 72; John Daly (US) 67, 73, 73.
214 – Steve Stricker (US) 77, 68, 69; Brandt Snedeker (US) 74, 71, 69; Ian Poulter (Britain) 71, 73, 70; Joe Durant (US) 71, 73, 70; Shaun Micheel (US) 73, 71, 70; Bob Tway (US) 71, 72, 71; Darren Clarke (Britain) 77, 66, 71; Tim Herron (US) 75, 68, 71; Corey Pavin (US) 74, 68, 72; Stewart Cink (US) 72, 70, 72; Heath Slocum (US) 72, 70, 72; Padraig Harrington (Ireland) 69, 73, 72; Troy Matteson (US) 72, 69, 73; Camilo Villegas (Colombia) 69, 71, 74.
215 – Brett Wetterich (US) 74, 71, 70; Richard Green (Australia) 72, 73, 70; Kenny Perry (US) 72, 72, 71; Shingo Katayama (Japan) 76, 67, 72; Retief Goosen (South Africa) 70, 71, 74; Graeme Storm (Britain) 65, 76, 74.
216 – Anthony Kim (US) 73, 72, 71; David Toms (US) 71, 74, 71; Hunter Mahan (US) 71, 73, 72; Rod Pampling (Australia) 70, 74, 72; Nick O'Hern (Australia) 72, 72, 72; Simon Dyson (Britain) 73, 71, 72; Bart Bryant (US) 74, 70, 72; Brett Quigley (US) 76, 67, 73; Will MacKenzie (US) 72, 70, 74; Paul Casey (Britain) 72, 70, 74; Paul McGinley (Ireland) 74, 66, 76; Pat Perez (US) 70, 69, 77.217 – Charles Howell III (US) 75, 70, 72; Phil Mickelson (US) 73, 69, 75.
218 – Colin Montgomerie (Britain) 72, 73, 73; Chad Campbell (US) 77, 68, 73; Tom Lehman (US) 73, 71, 74; Lee Westwood (Britain) 69, 74, 75; Niclas Fasth (Sweden) 71, 68, 79.
219 – Todd Hamilton (US) 73, 72, 74; Lucas Glover (US) 70, 75, 74; Robert Karlsson (Sweden) 73, 71, 75.
220 – Billy Mayfair (US) 76, 69, 75; Frank Lickliter II (US) 70, 75, 75; Thomas Bjorn (Denmark) 73, 71, 76.
221 – Brian Bateman (US) 71, 74, 76; Mike Small (US) 73, 70, 78.
223 – Ryan Benzel (US) 71 72 80.—Reuters