Taylor smashed her third ODI century, hammering a run-a-ball 120 as England racked up 259-6 from their 50 overs.
Australia got off to a good start with Shelley Nitschke and Lisa Sthalekar sharing 85 but England pegged them back with some fine fielding and bowling.
England bowled them out for 204 to go 2-0 up in the five-match series.
It was Taylor's day from the start as she continued her fabulous recent form, having struck 68 off 74 balls in the first match on Monday.
She put on 95 with Claire Taylor (42) and 86 with Beth Morgan as England reached 193-2, before she was eventually run out for 120, nine short of her previous best ODI score.
Ebony Rainford-Brent struck 30 off 32 balls to ensure England set an imposing target and Australia lost their first wicket with only two runs on the board, Leah Poulton caught and bowled by Katherine Brunt.
But Nitschke (47) and Sthalekar (43) knocked the ball around nicely and they were keeping up with the run rate too, until Laura Marsh (3-33) bowled Nitschke with a superb delivery which pitched on middle and leg and hit the off stump and Nicky Shaw got rid of Sthalekar.
From there the Aussies collapsed, as captain Jodie Fields ran herself out and the irrepressible Sarah Taylor produced two fine pieces of wicket-keeping to reduce them to 134-6, including a catch to dismiss Karen Rolton (32).
Laura Ebsary hit 38 as Australia managed to creep over 200, but when she was bowled by Shaw (3-39) it was all over.
The third ODI in the series takes place at Stratford-upon-Avon on Friday.