The defending champion was clearly tired after his extraordinary exploits on Friday and needed an hour and 47 minutes to overcome Sapsford.
The British No 2 had flown to Hannover to face Russia's Yevgeny Kafelnikov in the ATP World Championships after winning his quarter-final match against Jamie Delgado here and did not return until well after midnight.
Sapsford, ranked 210 in the world, and seeded fourth, looked as though he might succeed where Kafelnikov, the world No 6, had failed and, at 4-6, 1-2, Henman had to dig deep.
"I was not tired, physically as well as mentally, but Danny is an example to all youngsters of how to make the best of what you have," Henman said.
"I had to raise my game and I was pleased the way I did it. After what the sponsors and organisers had done to make my journey possible I didn't want to lose."
Henman broke back immediately for 2-2 in the second set with two unusual points in a row - a forehand stop volley which took a lucky net cord and then a high backhand smash which went for a winner from a tenacious Sapsford lob.
The world No 17 changed the pace of his game briefly but tellingly in the eighth game of the second set. Using more slice and coaxing his ground strokes with more consistency he made Sapsford play more balls to achieve the break of serve which gave him a vital cushion at 5-3.
Sapsford still managed to secure break back points in the final game of the second set and another crucial one, when Henman double faulted, in the penultimate game of the match.
When that disappeared with a scorching Henman forehand taken from the backhand side Sapsford's challenge was over.
"It was an unusual day yesterday and one I'm grateful for," said Henman, who says he will donate part of the pounds 100,000 Hannover prize money to a charity.
Henman will play Chris Wilkinson in today's final after he secured a 7-6 7-6 win against the second seed Andrew Richardson.Reuse content