The 37-year-old Woods posted his 17th career WGC victory, though it was only his first in four years. He has not won a major title in almost five years but hopes to change that with a win in the 77th Masters running April 11-14.
Not to be outdone, Matt Kuchar reached the semifinals for the second time in three years with steady play, rarely taking himself out of position.
Donald was the top seed in his quarter and third seed overall in the 64-man field behind world number one McIlroy and number two Woods, who both fell in the snow-delayed first round on Thursday.
Ireland's Shane Lowry, an old friend of the Northern Irishman from their amateur days, defeated the two-times major winner 1-up with the aid of chip-ins at the 11th and 12th holes at Dove Mountai.
McIlroy pulled one back at 14, but conceded the 15th after finding a series of bunkers. McIlroy then birdied the par-three 16th for a win, but they halved the last two holes with pars, and Lowry emerged victorious.
McIlroy, Woods, England's Luke Donald and American Brandt Snedeker would be top seeds if their ranking position holds.
After experiencing an emotional rollercoaster brought on by the recent death of his father and birth of his second daughter, Luke Donald didn't seem to have the appetite to play golf.
If he makes history this weekend and becomes the first golfer to win both the European and American money titles in the same season, Luke Donald said it would rank as his greatest achievement.
Arjun Atwal made a strong start with a two-under 68 to be placed at tied 18th along with Tiger Woods in the opening round of the WGC-Bridgestone Invitational at the Firestone Country Club, Akron.
Tiger Woods returned to competition after an injury layoff of nearly three months with a two-under 68 at the World Golf Championships Bridgestone Invitational on Thursday.
The spotlight's on the returning Tiger Woods at this week's Bridgestone Invitational, where defending champion Hunter Mahan is among the many wondering just what kind of golf the former number one will produce.
Tiger Woods has fallen out of the world top 20 for the first time since January 1997. The former world No.1 has not played since May 12 because of knee and Achilles tendon injuries although he is expected to announce later this week that he will return to action at the WGC-Bridgestone Invitational on Thursday week.
A tearful Thomas Bjorn returned to the scene of his former heartbreak on Thursday to grab the first round lead in the British Open which he shares with 20-year-old English amateur Tom Lewis.
For the first time in 11 months, Rory McIlroy walked off the 18th green in the early stages of a major championship and did not see his name atop the leaderboard.
Luke Donald is preparing to scrap his way to victory at the British Open as he seeks to crown his rise to the top of world golf with his maiden Major championship win.
Lee Westwood is confident he can slay the dragon of his Major championship jinx when he launches his British Open challenge at Royal St George's later this week.