The late-blooming O'Connell caused a major upset on day four of the Australian Open by downing No.13 seed Diego Schwartzman 7-6 (8-6) 6-4 6-4, while Inglis overcame a second-set blip to oust American qualifier Hailey Baptiste 7-6 (7-4) 2-6 6-2.
It guarantees the unheralded Australians $221,000 each in prize money, even if they bow out in the round of 32.
After claiming a marathon opening set in a tiebreak, O'Connell continued to play the big points better against the Argentinian counter-puncher.
O'Connell wrapped up the upset victory in three hours and seven minutes to set up a round-of-32 clash against American Maxime Cressy.
As is the case with O'Connell and Inglis, it will be the first time in the third round at any major for Cressy, who advanced by beating Czech qualifier Tomas Machac 6-1 3-6 6-1 7-6 (7-5)..
Schwartzman had reached the third round at Melbourne Park in each of the past four years and had never before lost at a grand slam to a player ranked as low as O'Connell, the world No.175.
But the Australian underdog was roared home to victory by a raucous home crowd on Court 3.
"I worked really hard in the Sydney heat in December so I was really happy when it was hot today," said O'Connell.
"Last year I played a pretty disappointing match on this court so I just wanted tio put in my best performance possible.
"I just wanted to channel the crowd's energy."
The atmosphere was just as charged over on Margaret Court Arena as the 24-year-old Inglis took control in the third set against Baptiste.
After clinching the victory, Inglis fell to her knees and shook her head in disbelief.
"This is so special, just playing on this court in front of this crowd," said Inglis.
"I can't believe it at the moment.
"This is my favourite court; the best court I've ever played on."
In another big opportunity, Inglis's third-round opponent will be either Estonia's Kaia Kanepi or Czech Maria Bouzkova, with both players unseeded.
