Donald, ranked No. 1 in the world and one of the event's four top seeds, never led in his match against Ernie Els, who trounced the defending champion 5 & 4.
Donald was one of just two players from the world's Top 10 to be eliminated on the opening day of the year's first World Golf Championship event. No. 6 Webb Simpson was knocked out by Matteo Manassero 3 & 2.
Neither Woods nor first-round opponent Gonzalo-Fernandez Castano played solid golf, with Woods struggling through a three-hole stretch beginning at the ninth in 4-over par. The former top-ranked player took a 1-up lead to the final hole, however, and he closed out Castano by making a 12-foot par putt after putting his second shot into a greenside bunker.
Woods will face Nick Watney in the second round after Watney defeated reigning British Open champion Darren Clarke 5 & 4.
Thirteen of the 32 first-round matches at the Ritz-Carlton Golf Club went to the 18th hole and seven other matches were not decided until the 17th.