Khawaja hung in there and scored a watchful 88 off 129 balls while Carey complemented his fellow southpaw in fine fashion and scored a 72-ball 71 to take Australia's score to 243/9 from their 50 overs at Lord's.
The defending champions lost half their side with less than 100 runs on the board, but a 107-run partnership for the sixth wicket between Khawaja and Carey helped them rebuild.
Australia were in dire need of a partnership and the duo of Carey and Khawaja provided just that with a century partnership, helping the defending champions to a respectable position.
Carey smashed 11 boundaries during his fluent knock, while Khawaja found the fence five times during his sedate innings.
And Finch couldn't thank them enough.
"Great partnership to get us to a competitive total by Khawaja and Carey. It was important that we get time in the middle. It was a difficult surface to play strokes on, and for Alex to get the ball off the middle was impressive," Finch said.
Following a recovery work from the duo, the Aussie bowlers came all guns blazing and after initial resistance from the Kiwis, they fell like nine pins thanks to the exceptional Mitchell Starc (5/26) and a miser Nathan Lyon (1/36), thus securing a massive 86-run win.
"It was also a good surface for Lyon to bowl, I thought, and he bowled really well. Important to bowl the part-timers too. It gives you a lot of wicket-taking options in the 20-40 over period," Finch said.
"It helps the team so much to get wickets in the middle-overs, like Starc, who can just return and take wickets immediately," he added.
Courtesy of the win, Australia remained on top of the table with 14 points from 8 games and now have one game to play. New Zealand on the other hand, have now lost two in two and will need to win their next one against England to confirm their spot in the semi-finals without any major hiccup.