England were bowled out for 249 in 48 overs in reply to Australia's 298 all out, with James Faulkner taking 3-31 as the tourists signed off their trip with a decisive win.
Watson's eighth one-day hundred was the decisive factor as Australia won their first trophy of an English summer in which they have contested the Champions Trophy, the Ashes and this five match series.
Two matches were rained off but wins in Manchester and Southampton were enough for Michael Clarke to get his hands on the silverware.
Watson hit 143 from 107 balls with 12 fours and six sixes, passing 5,000 one-day runs in the process and Clarke made 75 as the pair shared a partnership of 163 for the fourth wicket.
England were never up with the rate as Australia's bowlers kept them pinned down until Ravi Bopara and Jos Buttler had a brief flurry in the batting power play.
They took 26 off two overs but when Buttler went for 42 and Bopara for 62 the win was in the bag for the tourists as England fell away.
England's reply had got off to the worse possible start when Kevin Pietersen was run out for nought after not responding to Michael Carberry's call and they were always behind the rate losing wickets steadily.
Danger man and England captain Eoin Morgan had edged to 30 before he came down the wicket to Adam Voges and was stumped and the last obstacles between Australia and victory were Bopara and Jos Buttler.
But Buttler was bowled by Faulkner and Bopara was brilliantly caught by Voges at mid-off off a stinging drive to give Johnson his 200th one-day international wicket after being brought back by Clarke.
Watson's century was the bedrock of Australia's total which looked to be heading beyond 350 when he and Clarke were batting.
They rushed the tourists' score from 150 to 200 in just 32 balls and took a heavy toll on spinners James Tredwell, who went for 38 off four overs and Root, who conceded 58 runs off six.
Watson hit Root for 26 off one over - including three sixes into the stand at midwicket.
The pair's stand of 163 - a record for one-day internationals at this ground - kept England on the back foot until Clarke was caught at mid-on for off Chris Jordan.
Ben Stokes had Watson caught behind by Buttler and finished with 5-61 from 10 overs - the best figures at the ground by an Englishman.