Olesen, a student at the University of Arkansas, revelled in the links test and staved off the gallant challenge of fellow championship debutant Sample.
The 25-year-old had holed a couple of terrific putts around the turn, but Sample continued to put up a spirited resistance.
A wild tee shot on the 15th hole, however, saw the New Yorker slip one hole behind, and Olesen pressed home his advantage with a birdie on the 16th.
With Sample toiling in the bunkers up the 17th, Olesen wrapped up the match in style with a fine approach which kissed the flag.
In the morning’s quarter-finals, Olesen claimed the notable scalp of Scotland’s Walker Cup player Calum Scott on the final green.
The Dane had been two-down with just four to play but Scott stumbled to a trio of bogeys at 15, 16 and 17 as the match turned on its head in the last knockings.
Clemons, meanwhile, edged through at the 20th hole against Germany’s Laurenz Schiergen.
In a fascinating match of fluctuating fortunes, Clemons, who had been two-up after a brace of birdies at the first and second, found himself on the back foot late on when he missed a short putt on the 16th to fall behind for the first time.
Schiergen, aiming to become only the second German to reach the Final, had a chance to win it on the 17th but missed from eight feet.
Schiergen then had a three-footer on the 18th to seal a last four-berth, but his putt lipped out. Clemson was handed an unlikely reprieve and went on to win at the second extra hole.