The Pakistan-born Khawaja, playing his first Test since the 2019 Ashes series in England in place of COVID-isolated Travis Head, was at his unflappable best in notching an unbeaten hundred to put Australia in charge at 321 for six at tea.
Set 468 runs to win, England was bowled out for 192 with 21 overs remaining on the final day of play in the day-night test at Adelaide Oval.
After heavy defeats in Brisbane and Adelaide, the visitors must win in Melbourne to keep the five-Test series alive, with Australia only needing a draw to retain the urn as holders.
After restricting England's second innings to 297, the Australians needed just 20 runs to clinch the match. They did it in 5.1 overs, for the loss of only makeshift opener Alex Carey (9), with Marcus Harris (9 not out) hitting a boundary to finish off.
It is an even harder task at the Adelaide Oval, where Australia's 315 for six to defeat England in 1902 remains the best fourth-innings run chase. England's problems stem from being bowled out, after a batting collapse, for 236 on Saturday in reply to Australia's 473 for nine declared.
“Got to be kidding re Alex Carey,” 128-Test veteran Waugh tweeted. “For me Alex missing the squad is the biggest shock particularly after his batting during the World Cup
Australia captain Tim Paine won the toss and chose to bowl in the fifth Ashes Test at the Oval on Thursday as they chase their first series win in England since 2001.
The opener was fielding in front of the Hollies Stand on Saturday when the crowd started shouting: "He's got sandpaper in his hands!"