Captain Michael Clarke added 75 in a 163-run partnership with Watson for the fourth wicket, leaving England a tough target to clinch the series 2-1.
With the series all square at 1-1, Australia — in the final match of their lengthy tour — slumped to 48 for three before all-rounder Watson, who made 143, and Australia captain Michael Clarke (75) put on 163 for the fourth wicket on a ground where they’d both once played for Hampshire.
However, no other batsman made more than opener Aaron Finch’s 26 as Australia fell short of a total in excess of 300 that seemed well within their grasp.
Durham all-rounder Ben Stokes led England’s attack with five wickets for 61 runs — the 22-year-old paceman’s maiden five-wicket haul in 10 ODI matches.
England debutant Chris Jordan, in for fast bowler Steven Finn (side strain), took three for 47 after his first ball in international cricket was hit for four by Finch, whose last visit to this ground saw him score a Twenty20 world record 156 against England on August 29.
Jordan struck when he had Phil Hughes (two), opening in place of the injured Shaun Marsh, top-edging a pull to Michael Carberry at midwicket.