His unbroken stand of 77 with Brad Haddin (22) helped Australia reassert their superiority after an England-dominated middle session during which Finn and James Anderson (2-40) cut through the hosts' middle order.
Kevin Pietersen made the top score with 40 before getting out in the 22nd over and, after Eoin Morgan and Paul Collingwood departed cheaply, England were heading for an even bigger defeat until last-wicket pair Steven Finn and James Anderson put on 53.
Of the eight top pace bowlers in the world since January 2010, four were English - Tim Bresnan, James Anderson, Chris Tremlett and Steven Finn - with more than 200 wickets between themselves during this period.