Taylor made 101 to lift his team to 300 for eight and Australia struggled under the lights against the England spinners before being bowled out for 207 after 44 overs.
Opener Jason Roy scored 63 off 45 balls to give England a fast start before captain Eoin Morgan and Taylor shared a third-wicket partnership of 119 to put the hosts in a good position to make a huge total.
Morgan, however, was caught by Mitchell Starc off Glenn Maxwell for 62 and his side struggled to accelerate in the closing overs.
Ben Stokes, Jonny Bairstow, Moeen Ali and Liam Plunkett fell cheaply and although Taylor completed his maiden international century, he hit only five fours and was dismissed by Starc before England scrambled to get to 300.
Australia made a positive start to their reply, Aaron Finch making 53 and Steve Smith 25 before the Australian captain was brilliantly caught by Steven Finn one-handed at mid-wicket off leg-spinner Adil Rashid.
"It was amazing. I couldn't believe it," Morgan told Sky Sports. "Ben Stokes was in my eye-line and all I saw was a 6-foot-8 giant leaping.
"I've known Steven Finn since he was 15 years old and I've never seen him take a catch like that."
Wickets fell regularly under the lights as spinners Moeen and Rashid bowled cleverly and the Australian batsmen were unable to break the shackles.
"I'm very impressed," said Morgan. "We improved in the areas I asked the guys to from the first two games. Jason Roy played his game, lots of strong shots down the ground and then me and James Taylor got a good partnership going."
Smith said England had made a good total.
"They got a few too many," he added. "With the bat we struggled in the middle overs.
"The wicket was getting slower. We have to find ways to rotate the strike in the middle overs and then keep enough wickets in hand so we can go berserk at the end."
The fourth match in the five-game series is in Leeds on Friday.
(Reporting by Ed Osmond,; Editing by Tony Jimenez)
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