At 5-5 in the second set and with Paszek about to break the defending Dubai champion's serve, Henin unleashed one of her trademark backhand topspin cross court drives to save the break point and go on to win the set, and match.
"She was playing very well and I was not feeling comfortable on court," said a relieved Henin.
"I was very nervous and I was way from my best level, but I kept a good attitude and that was important for me.
"Even if I can't take 100 percent from that, it's good to keep fighting," added the 24 year-old.
"I knew it might be difficult because she is young and with nothing to lose, and I am coming through a very, very difficult time in my life.
"It takes time to find myself again. It isn't easy."
Paszek took the game to Henin, hitting flat and hard, to give a big scare to the former world number one.
16 year-old Tamira Paszek gained valuable
experience against the world number two [EPA]
"I just couldn't move to that ball on the break point in the second set," she said.
"But it was my first time on the centre court in a big tournament and I was very pleased with the way I played.
"In the end I was very tired. I have played five matches in five days and I am 16 and my legs are sore. But this was a great experience for me."
Henin will now face surprise packet Eleni Danilidou in the quarter final after the Greek player came from behind twice to defeat first round opponent Na Li from China and second round rival Ai Sugiyama from Japan.
Danilidou has won two out of three matches with Henin, and is looking to continue her run of form after ousting seventh-seeded Li and former top-ten player Sugiyama 5-7, 6-1, 7-5.
Big guns through to quarters
In other matches, second seed Amelie Mauresmo easily accounted for Russia's Vera Dushevina 6-2, 6-2, and will meet Slovakian eight seed Daniela Hantuchova in the quarters after she beat Maria Kirilenko of Russia in three sets, 2-6, 6-4, 7-6.
Swiss sixth seed Patty Schnyder also came from one set down to defeat Australian Alicia Molik 4-6, 6-2, 6-4, to set up a quarter final match with third-seeded Russian Svetlana Kuznetsova, who beat Meghann Shaughnessy 6-1, 7-6.
Finally, Serb Jelena Jankovic will meet Martina Hingis in the other quarter final after getting past Italy's Mara Santangelo 6-3, 7-5.
Hingis earlier had a scare against Spain's Anabel Medina Garrigues, who is ranked 33 in the world, fighting back from one set down to win 5-7, 6-3, 6-4.