The hosts made it 2-2 with one to play as they chased down 300 for the first time against Australia and only the fourth time in their history, with skipper Eoin Morgan leading the way with 92.
But Maxwell was irresistible – taking a two-phase boundary catch that will linger long in the memory, another one-handed grab to dismiss Morgan, one wicket and top-scoring for his side with 85 in their total of 299 for seven.
He did not deserve to be on the losing side but the hosts secured a brilliant three-wicket success with ten balls remaining, David Willey ending it emphatically with a steepling six down the ground.
James Taylor and Ben Stokes chimed in with twin 41s, while Moeen Ali contributed a controlled 21 not out at the close as England set up a series decider at Old Trafford tomorrow.
Afterwards Morgan praised his side’s run chase. He said: “It was hugely significant and two out of the four times [scores in excess of 300] has been chased down by this squad.
“At the halfway stage we were pretty confident we could chase it down. Before a ball had been bowled I certainly would have taken 300 as a chase and the guys were pretty optimistic about it.
“So to come out and have contributions and partnerships by the majority of our team was a great chase.
“Moeen Ali at the end with a very cool head seeing us home was great. It is always comforting having guys down the order that can play well and have a lot of experience of it.”