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England, who lost the first two ODIs to the Baggy Greens, won the toss earlier this afternoon and opted to bat first in Manchester.
Alex Hales was the first man to fall as he chipped the ball to Mitchell Marsh off the bowling of Glenn Maxwell when on nine. Opening partner Jason Roy fared better, bringing up his half-century off 34 balls.
He fell soon after on 63, giving Ashton Agar his first one-day wicket when he lofted a catch to Maxwell.
Taylor and Morgan both notched half-centuries of their own as they took England past 200, although the latter's innings came to an end on 62 when he was caught by Mitchell Starc off the bowling of Maxwell.
Ben Stokes made a brief 14 before he was caught by Aaron Finch, while Jonny Bairstow posted 17 prior to being run out by Steve Smith. Moeen Ali and Liam Plunkett both fell for one in quick succession as the England wickets began to tumble.
Taylor, though, remained at the crease and notched his first ODI century off 112 balls with a quick single. He added just one more run to his total before he gave Starc his first wicket of the innings, chipping a delivery to Agar for the catch.
Chris Woakes (14*) hit Starc over mid-wicket for six in the final over to take England to 300-8 at the end of their innings.