The pair share the first round lead with unheralded Swede Henrik Stenson on the Firestone Country Club’s classic South Course.
Building on the momentum from a strong fourth place finish at the U.S. PGA Championship, Woods launched his bid for a fourth title here with a flawless opening round.
Singh returned an almost equally tidy scorecard that included a single bogey but Stenson, playing in just his second event in the United States, had a more adventurous afternoon mixing seven birdies with three bogeys to get to his 66.
Only nine players in the elite 72-player field managed to scrape in under par on a sun-bathed opening day.
Lurking one stroke back at three-under 67 are Briton Nick Dougherty and Americans Davis Love III and Chris DiMarco, who lost in a playoff to Woods at the Masters earlier this season.
Spain’s Sergio Garcia and Australian Stuart Appleby and Nick O’Hern sit two shots adrift at two-under 68 while PGA champion Phil Mickelson, Chris Riley and Britain’s Luke Donald all finished on one-under 69.
First round scores
66 - Tiger Woods, Vijay Singh, Henrik Stenson
67 - Chris DiMarco, Davis Love, Nick Dougherty
68 - Stuart Appleby, Sergio Garcia, Nick O’Hern
69 - Phil Mickelson, Chris Riley, Luke Donald
70 - Mark Hensby, Zach Johnson, Colin Montgomerie, Kenny Perry, David Howell, Adam Scott, Thomas Bjorn, Kazuhiko Hosokawa, Sean O’Hair, Brent Geiberger
71 - Marc Cayeux, John Daly, Rod Pampling, KJ Choi, Fred Couples, Kenneth Ferrie, David Toms, Mike Weir, Paul McGinley Tim Clark
72 - Niclas Fasth, Ted Purdy, Jose Maria Olazabal, Stewart Cink, Chad Campbll, Steve Elkington, Ryan Palmer, Thomas Levet, Michael Campbell, Jim Furyk, Justin Leonard
73 - Woody Autin, Ian Poulter, Thongchai Jaidee, Scott Verplank, Rory Sabbatini, Tom Lehman, Trevor Immelman, Lee Westwood
74 - Stephen Ames, Stephen Gallacher, Stephen Dodd, Peter Lonard, Fred Funk, Geoff Ogilvy, Bart Bryant, Ben Crane
75 - Shigeki Maruyama, Paul Casey, Angel Cabrera
76 - Miguel Angel Jimenez, Darren Clarke, Richard Green, Jay Haas, Padraig Harrington
77 - Retief Goosen
79 - Craig Parry, Jyoti Randhawa
80 - Tim Petrovic
WD - Graeme McDowell.—Agencies