Bjorn yesterday followed up his first round victory over Masters runner-up Len Mattiace by beating Masters champion Mike Weir by a convincing five and four margin.
Curtis, without a top 10 finish before or since his amazing out-of-the-blue triumph at Sandwich, defeated fellow American Chad Campbell five and three.
The other semi-final is the expected one between world number two Ernie Els, seeking a record-equalling fifth title, and number three Vijay Singh. But both had to work hard.
Els was five up with six to play on fellow South African Tim Clark, but lost the next four holes and survived on the last, while Singh was taken to the 38th before getting the better of US PGA champion Shaun Micheel.
“I don’t have any unfinished business with Ben Curtis at all,” said Bjorn.
Curtis commented: “I don’t think Thomas will be looking for revenge. He just wants to go out and win.”
Weir never led Bjorn and was six down with 10 to play before mounting a mini-revival. He birdied the 27th and 29th and might have eagled the next had his opponent not conceded him the hole.
Having given himself a sniff of a chance, however, the Canadian left-hander extinguished his hopes with bogeys at the following two holes. “I was very determined to put the pressure on Mike. You never feel in control against a player like him, but I didn’t make any big mistakes,” said Bjorn.
Curtis’ first competitive shot in Britain since his Open win was a shocker, a hooked drive that left him needing a three-wood to the green whereas others were hitting wedges and even sand-wedges.
By the fourth, he was two down, but a superb inward half of 32, five under, took him ahead. The 11th, 12th and 17th were shared in birdies, but Curtis, having chipped in on the 17th, won the last with an eagle after a superb five-wood to 12 feet.
Campbell chipped in himself two holes later, but Curtis started making the crucial putts, going to the turn in 32 and adding another birdie at the 30th, where his opponent missed a four-footer.
After bogeying the 32nd by three-putting from off the green, Campbell carved his next drive into trouble and conceded the hole before Curtis even reached the green.
Els said after his escape: “It was a helluva match and Tim should feel proud of himself. I thought I had it won, but he played great down the stretch.
“I responded well and maybe it’s something I needed going into the weekend. I hope it gets easier, but I don’t think it will.”
Micheel was three-up with 13 to go, then one down after 28, but he birdied the 14th and 16th to go ahead again.
Then, however, he put two balls out of bounds at the next, first off the tee and then with his fourth shot. Singh was in trouble himself with his drive, but did not have to putt.
Both birdied the par five 36th and then Micheel, having missed a 14-foot chance to win at the 37th, found sand at the next and failed to get up and down.
Singh denied Els a fourth successive victory in the tournament in 1997, but the South African won their other two meetings. “I’m looking forward to it,” said Singh.