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Watson grabbed three wickets as Ireland were restricted to 123-7 and then smashed 51 off 30 balls to help Australia surpass the modest total in the 16th over of the group B match.
The New South Wales all-rounder put on 60 for the first wicket with David Warner (26) in seven overs, and 31 off 18 balls for the second with Michael Hussey, before he was run out in the 11th over.
Watson, who hit five boundaries and three sixes and claimed a wicket with his first delivery, was named the man of the match.
"We knew how important the game was to make a statement," he said. "I had been thinking about how to bowl the first over for about a day and it worked out nicely."
Barely 3 000 spectators were present at the 35 000-capacity Premadasa stadium to watch Australia teach the non-Test nation a cricketing lesson in the first ever T20 clash between the two sides.
Australia, who lost to England in the final of the 2010 World T20 in the Caribbean, had briefly slipped below Ireland in the T20 rankings earlier this month.
The slump started with the first ball of the innings, which skipper William Porterfield hooked down fine-leg's throat to the great delight of bowler Watson.
"We did not have a great start; we tried to get a platform but that did not happen," said Porterfield. "I can't fault the lads because they tried their best."
Ireland's decline continued as in-form batsman Paul Stirling was caught at third man off Mitchell Starc and Ed Joyce holed out to mid-off against Glenn Maxwell after making 16.
Left-arm spinner Brad Hogg, the oldest player in the tournament at 41, struck with his second delivery when he trapped Gary Wilson leg-before for five.
Kevin O'Brien top-scored with 35, adding 52 for the fifth wicket with elder brother Niall (20) after Ireland had slipped to 33-4 by the eighth over.
The O'Brien brothers were dismissed in the space of four balls from Watson.
Australia play the West Indies in their final group game in Colombo on Saturday. Ireland take on the West Indies on Monday.
Two teams from the group will advance to the Super Eights round.
Brief scores:
Ireland 123-7 in 20 overs (K. O'Brien 35, N. O'Brien 20, E. Joyce 16, S. Watson 3-26, M. Starc 2-20). Australia 125-3 in 15.1 overs (S. Watson 51, D. Warner 26)
