A rollicking match at the Melbourne Cricket Ground was won late on day five when the home side blasted out seven Indian wickets in the final session.
Cummins was named player of the match for his all-round deeds, including taking three key wickets on the final day as the tourists were skittled for 155.
He did it in front of a final-day crowd of nearly 75,000, pushing the combined attendance across five days to 373,691, easily the highest for any match played in Australia.
The 66-Test veteran said he agreed with several team-mates that the Test was among the best they'd played in.
"I just felt everyone was talking, trying to work out where it sits. I reckon that it's right at the top," Cummins said.
"When you take it all into account, it's probably the best Test match I've been involved in.
"I don't know what the crowd was today, but it was huge," he added at the press conference.
"It felt like the match swung a lot as well. It never felt like we were so far ahead of the game that a win looked certain.
"So overall, just one of those great wins."
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