Cummins and Lyon forged an unbroken partnership of 55 runs for the ninth wicket to take Australia home.
Chasing 281 to win, Australia were 107/3 at the close of play on Day 4 with Usman Khawaja (34*) and Scott Boland unbeaten in the middle.
Heading into the final day, the hosts needed seven wickets and the tourists required 174 more runs to win the contest. As it turned out, the match went down to the wire.
Boland, who was unbeaten on 13 overnight, managed to add 7 more runs to his tally before being dismissed by Stuart Broad on Day 5. The likes of Travis Head (16), Cameron Green (28) and Alex Carey (20) got out after getting set while Khawaja fell for 65 as Australia slipped to 227/8.
With England inching closer to victory in the final session, Australia skipper Pat Cummins was joined by Nathan Lyon in the middle. They had a tough task at hand as the visitors still needed 54 runs to get over the finishing line.
Amid the pressure situation, Cummins struck an unbeaten 44 and was well supported by Nathan Lyon who made 16 not out in an unbroken partnership of 55 runs for the ninth wicket to take Australia home.
Cummins hit the winning boundary against Ollie Robinson and followed it by dropping his helmet and bat in wild celebration before running towards Lyon to lift him up, rejoicing the narrow win.
For holding their nerves in pressure situations, Pat Cummins and his men received rich praise from the cricket fraternity on Twitter.
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