Ben Duckett cracked 165 off 143 balls to lift England to 8-351 on Saturday night, bettering the previous best Champions Trophy mark of 4-347 set by NZ against the US at The Oval in 2004.
But England's record lasted only a matter of hours, with Australia chasing down the victory target on 5-356 with 15 balls to spare courtesy of Inglis' heroics.
The Leeds-born wicketkeeper cracked an unbeaten 120 off 86 balls, including eight fours and six sixes, in a monumental performance.
Fellow keeper Alex Carey (69 off 63 balls), opener Matt Short (63 off 66), Marnus Labuschagne (47 off 45) and Glenn Maxwell (32no off 15) all produced important cameos to ensure Australia's campaign got off to a winning note.
Australia face South Africa on Tuesday and Afghanistan on Friday, and one more win may be enough to secure a semi-finals berth by finishing in the top two in Group B.
"I'm over the moon, great win," Inglis said.
"We knew it was going to be tough going up against England, and 350 - a lot of things have got to go right to chase that down.
"I'm just really pumped on a personal level, and for the guys out there it was a great performance.
"It's only a short-sharp tournament, so to go one from one is really important."
Duckett smashed 17 fours and three sixes in his electric knock, making the most of Australia's decision to bowl first on a batter-friendly wicket.
Joe Root chipped in with a handy 68 off 78 balls, combining with Duckett for a 158-run partnership.
Duckett set an individual record, with his total the highest ever in Champions Trophy history, bettering the 145 from Kiwi Nathan Astle against the US in 2004.
Carey, normally in gloves, proved the surprise star in the field for Australia with three catches - two of them screamers.
The 33-year-old stunned the crowd with a diving, one-handed catch at mid-on to dismiss opener Phil Salt for 10 in the second over.
He proved it wasn't a fluke later in the innings by taking a brilliant diving catch to dismiss Harry Brook for three.
Australia's run chase then got off to a poor start.
Travis Head was caught and bowled by Jofra Archer for just six, and Australia were 2-27 when Steve Smith edged a Mark Wood 151km/h thunderbolt to slip.
Labuschagne entered the tournament under a mountain of pressure to perform, and his 95-run stand with Short put Australia back on track.
But the pair's dismissal within 14 runs of each other left Australia in strife at 4-136, before wicketkeepers Carey and Inglis took the game away from England.
Inglis in particular was destructive, with his vast array of strokes and ramps leaving England players visibly frustrated.
Australia were 4-248 when Archer dropped an easy catch in the outfield when Carey was on 49, with the missed chance proving to be a dagger blow for England.
It helped Australia post the second highest ODI chase in their history, only behind the 6-359 they recorded against India in 2019.
It also marked the highest men's run chase in ICC tournament history.
