Asked to bat first, England rode on an unbeaten century from Jos Buttler to post 302/6 in their 50 overs.
Buttler raised an 83-ball hundred from the last delivery of the innings as they crossed 300 - a score that looked unattainable for most of the proceedings.
Smith was given out caught behind off Chris Woakes, with the England keeper claiming a low catch with the Australian captain on 45.
Needing conclusive proof to overturn the on-field decision, the third umpire Kumar Dharmasena chose to back in his umpires, despite replays appearing to show the ball touching turf as it bobbled in Buttler's glove. The video created quite an uproar on social media with few suggesting that the Australian skipper indulged in ball-tampering by applying the lip balm to the ball.
The match wasn't without controversial moments, particularly when Wood claimed the coveted wicket of Smith.
England had won the first two matches chasing down Australia's totals and perhaps that was on Smith's mind when he elected to bowl after winning the toss.More news: Jamaica declares emergency in Montego Bay
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Smith left the field shaking his head, having five minutes previously been happy to walk off after seeing Buttler take the grab.
"I don't know what it is, but not many balls were hitting the middle of my bat which was disappointing ..."
Josh Hazlewood and Pat Cummins made a difference though in their return to the fold, but Mitchell Starc went wicketless. He said he would prefer a system where the third umpire made a ruling based purely on the pictures in front of him.
The difference was visible straight away as Cummins accounted for Jason Roy in only his second over to create the first opening and Zampa cleaned up Bairstow after both of them had starts worth 19 and 39 respectively.
The home side's run-chase got off to a shaky start as David Warner (8) and Cameron White (17), who was bumped up to number three in the batting order, were back in the hut with 44 on the board.
After coming unstuck on a similar surface in Cardiff during the 2017 ICC Champions Trophy semi-final, Morgan pointed to the contrast in displays then and here in Sydney.
Before play, England batsman Joe Root was presented with his 100th ODI cap from fellow Yorkshireman Sam Burgess, a rugby league player for England and South Sydney.