Seeded 15th in the tournament, Micheel opened up a huge advantage on the seventh-ranked Donald, the highest-seeded player remaining, and held off a late charge to win 4 and 2.
Thursday, he did the field a favor by offing Woods to end the world No. 1's winning streak at five tournaments. In the quarterfinals on Friday, he led by as much as 7-up on Donald.
Donald's exit leaves No. 9 Colin Montgomerie the highest-seeded player remaining in the field. Montgomerie, who is also the only former Match Play champion left, knocked off defending champion Michael Campbell, 1-up, with a birdie on the 36th hole.
Montgomerie also beat David Howell in the first round with a birdie on the last hole. On Saturday he will face Paul Casey, who was a 5 and 3 winner over Mike Weir.
Micheel will play Robert Karlsson, who was an easy 4 and 3 winner over Angel Cabrera in the quarters.
With Ryder Cup teammates Woods and Jim Furyk making early exits this week, Micheel is the lone American remaining with a chance to become the first U.S. winner since Mark O'Meara bested Woods in 1998.
He took a 5-up lead on Donald after 18 holes, mostly due to Donald's inability to make many birdies early.
Micheel made eight birdies and one bogey on the first 18 holes, consistently knocking approach shots close on the way to a 65 at the Wentworth Club's par-72 layout. Donald didn't drop any shots, but he made just two birdies for a 70.
'Early in the round he just didn't make any putts,' Micheel said.
Micheel extended his lead to 7-up after 20 holes when he birdied the par-3 second. His momentum slowed towards the end of the match, however, and Donald made a 6-foot par putt at the 15th to trim Micheel's lead to 3-up after 33 holes.
But Micheel was able to clinch the match with a birdie on the next hole, the par-3 16th, where Donald could only make par from the rough.
'I played well,' Micheel said. 'I think it's difficult when you have such a big lead. It wasn't that I played differently (down the stretch), I just played a little more conservatively, particularly with my club selection.
'Short of making a few more birdies on the back nine, I'm really pleased with my round.'
Montgomerie fell 4-down early in his match after the top-seeded Campbell rolled in a 40-foot eagle putt at the par-4 fourth.
But the 1999 champion made birdie putts of 15 feet at the eighth and 3 feet at the ninth to pull within 2-down around the turn. He then added birdies at 14 and 16 to square the match after 18 holes.
Campbell bogeyed the par-3 second to give Montgomerie a 1-up lead after 20 holes, and the match was close after that. Campbell was able to even it three times without taking the lead, the last time coming when Montgomerie missed a long birdie putt at the 17th.
At the 36th and final hole -- the par-5 18th -- both players landed in the same greenside bunker, just inches from each other.
Campbell's next shot hit the rim of the bunker and fell back in, while Montgomerie knocked his within 10 feet to set up a birdie for the win and the match.
'If I had missed (the putt), he would have had his 5-footer for a half and we could well have been on our way to the 37th hole,' said Montgomerie. 'I had to get mine in and I did. It was a good victory but I'm very tired.'
Casey, the 12th seed, had a close match with the 13th-seeded Weir until taking the lead for good when Weir bogeyed their 22nd hole, the par-5 fourth.
Weir struggled with back pain, was visited by medical personnel at the 15th hole, then missed an 18-foot par putt there to give Casey the win after 33 holes -- sending Casey to a meeting with Montgomerie.
'He should be the favorite as he knows this place very well,' Casey said of Montgomerie.
Karlsson, a Ryder Cup rookie, trailed Cabrera for only one hole early in their match. Cabrera made two double-bogeys in three holes at the end, finally missing a left-to-right, 6-foot bogey putt at the par-4 15th to give Karlsson the match after 33 holes.
'My short game has been good and has been the key to my success so far,' said Karlsson, who knocked off Furyk on Thursday. 'I holed a few fantastic putts today and chipped in once yesterday...overall my chipping and short game have been good.'