Having already seen off compatriot Lee Westwood earlier in the afternoon, Willett got off to a strong start with three early birdies to move two up after five holes.
A three-putt from 15-feet at the par-four sixth temporarily halved Willett???s advantage, although that was soon restored when Fleetwood???s approach shot at the next landed short of the green.
Willett opened the back nine with a bogey after missing a nine foot par-save, but quickly found himself four clear thanks to a tap-in gain at the 12th as Fleetwood dropped shots at the 11th and 14th.
With Fleetwood needing a birdie at the next to keep his slim hopes alive, the world No 57 was unable to hole his 45-foot putt from the edge of the green.??
???I swung it really well, hit some good golf shots and putted nicely,??? Willett told Sky Sports 4. ???Everything was nice, neat and tidy; missed a couple of short ones in and around the middle which was a shame, but it was another good solid match.
???You never feel comfortable in this format, as you know everyone???s a good player that can very easily throw a few birdies at you, so we just tried to keep pressing.
???If anyone brings their A game they???re going to be difficult to beat regardless of who they???re up against.???
The world No 49 will now face Gary Woodland in the last four, with the American the first man through after completing a 5&3 win over John Senden.
Woodland opened with four birdies from the first five holes to take control, moving five ahead when Senden was unable to save par from 15-feet at the seventh.
The Australian made his solitary gain at the par-four 12th to cut the gap back to four and missed a 15-foot birdie chance at the 14th, before Woodland sealed the win with three holes to spare.
After rolling in a 10-foot birdie at the 15th complete victory, Woodland told Sky Sports 4: ???It was nice to get off to that good start and after that I played pretty solid, which kept the pressure on him (Senden) all day and allowed me to maintain that lead.
???You want to get out of there as quickly as possible, not only because it has been a long day but also because it???s cold and you don???t want to give anybody any hope.
???We have a long way to go but it???s nice to put myself in this position. I???ve had two weeks off, so had some time to dial some things in and it???s starting to pay off. ???