Morgan had been struggling for runs at domestic level earlier in the season, averaging 26 in Twenty20, 10.16 in first-class cricket and just 6.66 in the 50-over cup.
He came into the county season having had a busy period where he led England in their woeful 50-over World Cup campaign in Australia and New Zealand before heading to the Twenty20 Indian Premier League.
It led him to ask Fraser, his boss at Middlesex and also an England selector, if he could take some time off from playing for the Lord's-based county in a bid to get himself in the right frame of mind for England duty.
"Before the rest it had been about 11 months since I'd had a break, which is quite a long time to go," said Morgan.
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"If I'd have known I was going to be that busy in October, having the (England) captaincy role as well, I would have earmarked a break before then. I've never asked for a break before and this time Gus and Middlesex were exceptional.
"We earmarked this one-day series, I need to be fresh for that, so it's worked out well."
Australia captain Steven Smith was threatening to win the match off his own bat and had reached 90 off just 53 balls when Willey had him caught at mid-wicket.
Ashes-winner Stokes then held his nerve when, with Australia needing 12 off the last over, he restricted them to six runs.
Stokes also kept his cool to dismiss Nathan Coulter-Nile and complete two run-outs.
"I hadn't earmarked Ben, before the day had started, for bowling the last over of the game," Morgan said.
"It was a tough one but he took on the responsibility of bowling that over really well."
"He's brilliant," said Morgan.
"A bit like Stokesy he just loves responsibility, he likes the limelight, he doesn't shy away from taking it on.