England had looked dead and buried at 45-4 in their chase for 371 runs to level the series but Ben Stokes' majestic knock of 155 and Ben Duckett's 83 lifted them to 301-6.
Australia started to look ragged in the field before dismissing Stokes and knocking over the tail cheaply to move 2-0 up in the series and firmly on course to retain the Ashes.
"Another wonderful game, right down to the wire," Cummins said. "Stokesy gave us a few heart-stopping moments and the crowd seemed to enjoy it."
Cummins played in the 2019 Ashes test at Headingley when Stokes made 135 not out to inspire England to an extraordinary one-wicket victory.
"Of course, he played another great innings and I'm glad we got him out when we did," Cummins said.
"Having a world-class player like Ben on the top of his game, you start thinking 'that boundary looks short' - I was glad to have 200 on the board."
Australia were hampered by the absence of their main spinner Nathan Lyon who was unable to bowl after suffering a calf strain.
Stokes struck nine sixes and nine fours on a withering assault but Cummins said Australia had not panicked.
"Just trying to stay patient, have the fields out," he said. "He did well to keep getting himself on strike but we were happy with them going at two an over."
Cummins played down the furore surrounding the dismissal of Jonny Bairstow, stumped by wicketkeeper Alex Carey after leaving his crease at the end of an over.
Disgruntled MCC members verbally abused Australia players as they walked through the pavilion at the lunch interval.
"Emotions were running high and words were unfortunately exchanged by a small number of members," the MCC said in a statement.
Cummins said he had accepted the apology.
"They were quite aggressive and abusive towards some of our players, which I know the MCC weren't too happy with," Cummins said. "The MCC came and apologised for the behaviour of some of the members."
Australia only need to avoid defeat in one of the three remaining tests to retain the Ashes.
"We couldn't be in a better position," Cummins said.
Check out the full scorecard from the second test with Flashscore.
