England’s last four wickets added 145 on the final day to be all out for 352 and lose by 82 runs after finally showing some fight in the series as they chased a record 435 to win.
Australia’s Scott Boland removed last man Josh Tongue, caught by Marnus Labuschagne, to spark wild celebrations as the famous urn remained in Australian hands.
“It feels pretty awesome,” said Cummins.
“It wasn’t easy today, but we got it done. The last two months have been a bit of a grind.
“But it’s all worth it for days like this. That’s when we are at our best… it’s good old-fashioned grind, and I love the toil from all the guys.”
England had to win to keep the five-match series alive after being crushed by eight wickets inside two days at Perth and in four at Brisbane, with two more Tests still to play at Melbourne and Sydney.
Australia had one setback on Sunday when they lost spin wizard Nathan Lyon, who damaged his hamstring fielding and hobbled off after saving a boundary.
But he was not needed as seamers Mitchell Starc, Cummins and Boland wrapped up the innings either side of lunch with the second new ball.
Lyon was sent for scans and later seen on crutches, potentially putting him out of the Melbourne Test, starting Friday, and Sydney on January 4.
“It doesn’t look great. Don’t know yet, but seeing someone on crutches doesn’t really bode well for someone with a Test match a week away,” said Cummins.
“It’s going to be hard to replace him but we have some guys who have already had a taste of international cricket around the traps.”
England’s demise in 11 days of play is the joint second quickest in more than a century, since the 1921 Ashes was completed in eight days, with their “Bazball” style of ultra-attacking cricket exposed.
“That dream is now over, which is incredibly disappointing,” said England skipper Ben Stokes.
“Everyone is hurting and quite emotional about it. It hurts, it sucks, but we ain’t going to stop.”
Stokes also took some positives from the way England battled, having demanded more fight leading into the match.
“That stuff I wanted to see, I’ve seen that this week. I think we can take a lot from this game,” he said.
“We have got so much to play for, and we will be flying into these next two games.” (AFP)