Australia, albeit fielding a much-changed team ahead of bigger assignments on their northern tour, were forced to cling on desperately to secure a 19-15 win over Japan in Tokyo on Saturday.
The Wallabies led 14-3 at halftime but gritty Japan reduced the deficit to just four points with 20 minutes remaining to set up a stirring finish.
The contest was the visitors' first against their former coach Jones, who quit the Australia job to return to Japan soon after the Wallabies' calamitous 2023 World Cup campaign.
"What I'm super pleased about is that now we (Japan) are a team that stays in the fight," Jones told reporters. "We kept going, we could have won the game in the end but we weren't quite good enough."
Australia coach Joe Schmidt said of Japan's performance: "There was nothing surprising about how competitive they were, how combative they were."
Japan now travel to London to take on South Africa at Wembley Stadium next week.
"We're going there thinking we're going to win," a buoyant Jones said.
In his previous stint as Japan coach, the Brave Blossoms pulled off a legendary upset at the 2015 World Cup in England, beating the Springboks with a last-gasp try.
"South Africa are like everyone, if you put pressure on and get in their face they make mistakes," Jones said. "Imagine beating South Africa at Wembley, that would be iconic."
