Taylor, brought back after England rested Ashes-winner Joe Root from this series, was out for 101 having been left short of a hundred on 98 not out when England were beaten by eventual champions Australia at the World Cup in Melbourne in February.
The diminutive 25-year-old Nottinghamshire batsman, playing his 21st match at this level, faced 114 balls.
But it was a testament to Australia's accuracy that he only managed five fours.
And whether England, who at 2-0 down with three to play against world champions Australia after a 64-run loss at Lord's on Saturday had to win this match to keep the series alive, had enough runs on the board remained to be seen.
But the partnership would have been curtailed had not wicket-keeper Matthew Wade missed a stumping off ODI debutant spinner Ashton Agar when left-hander Morgan was on 15.
As it was Australia slowed England's run-rate, with a total of 200 for two in 32 overs, advancing only to 245 for four in the 43rd over.
After Taylor holed out in the last over, it needed some clean-hitting from Chris Woakes, including a six off Mitchell Starc, to take England to 300.
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