England defended the 163-run target in Southampton despite Australia once being 124/1.
In the 15th over of the chase, with Australia 124/1, wrist-spinner Adil Rashid gave England an opening by dismissing Steve Smith and Glenn Maxwell in quick succession.
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Morgan then made a brave move of bringing back Jofra Archer and Mark Wood for their respective final overs. He was immediately rewarded when another pair of quick wickets, this time a well set David Warner and wicketkeeper Alex Carey, exposed Australia's soft underbelly, their lower middle-order.
"We have talked as a side about making inroads and when we do, we have threats to take maybe two or three at a time," Morgan was quoted as saying by ESPNcricinfo after the two-run heist. "Some of our pace bowlers and Adil have posed that threat, making it particularly difficult for people coming in and facing them straight away."
"I think after Moeen's over, things started to turn for us. We got the ball reverse-swinging a little bit, but again, creating that opportunity with Adil getting Maxwell and Smith created that opportunity."
"I thought we might end up running out of our best bowlers earlier, but they seemed to continue to take risks, particularly against Adil and then Jof came back earlier as a consequence of that."
After openers Warner and Aaron Finch put on 98 of the 163 runs required in just 11 overs, Morgan realised he has to take a few risks and go for wickets rather than wait for the tide to turn itself.
"We needed to take wickets to try and stay in the game. I don't mind if we lose the game inside 16 overs. To try and win the game is the priority, so you have to chase your tail a little bit or come up with different things."
"I'm delighted the guys showed belief and courage to do something to take wickets, and that was displayed a lot in the last six overs when we held our length a lot because it was the hardest to hit."
"Over two years ago we would have gone to bowling yorkers or slower balls which would have brought Australia back into the game. It was great that we stuck to our guns."
Morgan reserved special praise for death-overs pacers Chris Jordan and Tom Curran for holding their nerves.
"In the winter it was very similar in New Zealand and South Africa where Chris Jordan and Tom Curran led the attack and took the responsibility," he said. "It is quite a weighty responsibility but they see an opportunity to take the team forward and lead the team and they do it very well."
"For Tom, the game that sticks out in particular is the game at Durban and then again tonight with him closing it out. We have shown a lot of faith in [Jordan] because he has earned it. He has been one of our greatest ever bowlers and only sits behind Broady in the lead wicket-takers. To have someone like that who is calm, even when he is not bowling and continuing to offer on and off the pitch."
"For younger guys coming through, I think he sets a great example and given he has only come back from surgery recently, he has done a great job," Morgan added.
(Inputs from ESPNcricinfo)