Neither managed a break in the first set, but Johansson opened up a 4-1 lead in the second after Hewitt double-faulted on break point.
The Australian struggled to hold serve in the fourth and sixth games, but then forced Johansson to save four break points to maintain his advantage.
"I worked very hard to hold that service game," Johansson said.
Johansson, who is ranked 446 and was awarded a wild card into the main draw, was put under pressure when he served for the match.
"I am a little surprised but I am also not surprised," Johansson said. "I have always had a good serve and this time I tried to play aggressive from the first point. I didn't give him any rhythm."
Mikhail Youzhny of Russia also advanced, beating seventh-seeded David Ferrer of Spain 7-6 (3), 6-2.
Ferrer broke his opponent in the second game to take a 2-0 lead but Youzhny won three consecutive games, eventually taking the set to a tiebreaker. The Russian, ranked 52nd in the world, held the serve to take the set.
Youzhny broke serve in the third and eighth games of the second set.
"I have been in Kuala Lumpur a few days and I think it helps me that I am more used to the conditions than he was," Youzhny said.
Indian qualifier Rohan Bopanna also caused a stir, beating Jose Acasuso of Argentina 4-6, 6-3, 6-4 on center court.
"At least I had played a few matches before this first round, whereas Jose was playing on this court for the first time," Bopanna said. "Certainly I am very happy about this win and it's a great boost for me."
Tomas Berdych of the Czech Republic survived a second set lapse to beat Igor Kunitsyn of Russia 6-1, 3-6, 6-2.
Also, Martin Vassallo Arguello of Argentina defeated Feliciano Lopez of Spain 6-3, 6-3, and Karol Beck of Slovakia defeated Mikhail Kukushkin of Kazakhstan 1-6, 7-6 (4), 6-3.
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