Serving for the match, and glancing at the clouds gathering overhead, he missed three match points before taking his win with a decisive backhand volley.
In the semi-finals tomorrow, Henman plays the South African Wayne Ferreira.
The British No1 said: "I wasn't able to play as well as I did against Wayne Arthurs in the last round for different reasons. Scrichaphan stayed on the baseline so I didn't have a target to hit at all of the time.
"The Ferreira game will not be easy but I am happy to have the opportunity," he said.
Ferreira, the 1992 champion, was in sharp form to beat the Dutchman Peter Wessels 6-3, 7-5.
Pete Sampras, twice champion and twice runner-up, went through to the quarter-finals with a 6-3, 6-4 win over the Dutch left-hander Jan Siemerink.
Sampras was on court twice last night before rain drove him off with a 2-1 lead. Today Sampras quickly took command against a player he had beaten four times before and only needed to work a fraction harder in the late stages when Siemerink saved four match points.
Sampras moved on to a quarter-final against fellow American Jan-Michael Gambill.
Hewitt, the 20-year-old Australian who beat Sampras in the final here last year, earned himself a quarter-final against Rusedski with a 6-3, 6-2 victory over Byron Black.
