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.
"The crowd were very, very good," he said "The last four games with the crowd noise, for me that was playing tennis at this level is all about.
"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."
