The British number one claimed the first set quite easily before letting his Argentine opponent David Nalbandian back into the match in the second, eventually running out a 6-2, 6-7, 7-5, 6-3 winner.
"After losing the second set tiebreak it was quite depressing to be sitting there at one set all after playing so well," said the 28-year-old of third set, when there were seven service breaks in a row .
"But I can take a lot of positives from that third set because, even though I couldn't hold my serve, I just kept positive and told myself that I would just break his serve again."
"Mentally it was like water off a duck's back, I just thought I'll go out and break him again."
Henman said the support from the fans on a packed Centre Court had really boosted him.
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"The crowd support has always been pretty incredible here, they choose their moments, they gave me such a lift, it was a pleasure to play in an atmosphere like that.
"It was a phenomenal atmosphere to play in and it was much appreciated."
Henman's quarter-final opponent has yet to be decided as the fourth-round match between French Open champion Juan Carlos Ferrero of Spain and Sebastien Grosjean was stopped for bad light on Monday with the Frenchman leading 6-2, 4-6, 7-6.
"I'll enjoy hitting a few balls tomorrow for 30 or 40 minutes and then watch them slug it out for a fourth and possibly a fifth set," the 10th seed said.
"I'm very happy to be in the position I'm in now. But I know if my level drops I'll be in trouble, so I've got to keep doing the right thing."