Australia, set 301 to win, were dismissed for 207 with six overs of their innings left.
Victory in this day/night fixture would have given the world champions an unbeatable 3-0 lead in the five-match ODI series.
But instead England -- who had lost 11 times in their previous 12 one-dayers against Australia -- cut the tourists' lead to 2-1 with two to play.
Off-spinner Mooen Ali and leg-spinner Adil Rashid shared five wickets between them, with Ali's three for 32 in his full 10 overs the all-rounder's best ODI figures.
Also Read
But fellow opener Joe Burns fell for nine when he chipped Steven Finn to England captain Eoin Morgan at mid-off.
Australia captain Steven Smith walked out to boos after upholding an appeal for obstructing the field that led to Ben Stokes's controversial dismissal at Lord's.
Having survived a tough chance because of the diminutive Taylor's lack of reach, Smith (25) was brilliantly caught when diving fast bowler Finn used his 6ft 7in frame to hold a stunning one-handed catch at short mid-wicket off Rashid.
His exit was the start of a mini-collapse that saw three wickets lost for 35 runs to leave Australia in trouble at 141 for five.
- Reverse trouble -
===================
Glenn Maxwell, after reverse-hitting Ali for two fours in as many balls, tried to make it three in a row only to miscue and be caught off a top edge by wicket-keeper Jonathan Bairstow.