The third seed, looking to become the first Australian to win the title since Mark Edmondson in 1976, wore down the 25th seed in two hours, 17 minutes to set up a meeting with Spanish teenager Rafael Nadal.
"I don't know if there was any (extra) tension," Hewitt said.
"We were playing a very tight third-round match in a grand slam, and he is a very tough opponent.
"I'm through to the second week now and this is the business end of the tournament."
The first three sets were of high quality but the match burst into life early in the fourth with some unsavoury scenes.
Chela appeared to get angry with Hewitt for his on-court gesticulations, fired a serve which the Australian had to jump to avoid being hit by.
After Hewitt had broken for a 2-1 lead, he seemed to mutter an obscenity towards Chela and the Argentine was then seen to spit in Hewitt's direction.
The spat galvanised Chela and he broke back for 4-4, only to drop his own serve immediately, and Hewitt held on to reach the last 16.
