The Northern Irishman was drawn alongside the 14-time major winner and the current world number one in a dream threesome for the crowds.
He shot a five-under 67 to hold the clubhouse lead alongside Swede Robert Karlsson.
"It was a good score and a great way to start 2012, but I don't feel I drove the ball particularly well and it's something I've got to work on," the US Open champion said afterwards.
"It was nothing that a good practice session won't fix."
Woods is just three shots back after a two-under round of 70, while Englishman Donald is a further shot adrift.
"It was fun to be part of that threesome - Tiger and Rory are huge names in the world of sport," Donald added.
Sergio Garcia produced the shot of the day by delivering a hole-in-one on the par three 12th, his first ace on the European Tour.