Set a modest 145 to win, Ireland, who in the first round beat Bangladesh, were on course at 87 for one before Andrew White holed out to Nuwan Kulasekara.
It was the start of a collapse that saw three wickets lost for four runs in seven balls with spinner Ajantha Mendis striking twice to get rid of Kevin O´Brien and brother Niall, who made a game 31 before he was stumped.
At 91 for four Ireland were in trouble and Lasith Malinga then took two wickets in two balls to reduce them to 105 for six.
But John Mooney (31 not out) kept Ireland in the hunt and off the last over, from the unorthodox Malinga, they needed 18 to win - a target that proved beyond them as they finished on 135 for seven
A fine all-round display in the field saw Ireland, who at the 2007 World Cup in the Caribbean beat both Bangladesh and Pakistan, restrict Sri Lanka to just 144 for nine.
Only former Sri Lanka captain Mahela Jayawardene´s 78 prevented complete collapse in an innings where only three batsmen made double figures and the next best score was Sanath Jayasuriya´s 27.
"Mahela was brilliant. He´s been doing this for years and he was nearly at his best today," said Sri Lanka skipper Kumar Sangakkara.
Ireland captain William Porterfield believes with more experience his side could have won.
"We bowled really well to restrict to them to 144. We got a decent start with the bat but just couldn´t pull through," he said.
"We are learning with every game. With more experience we could have pulled through."
Brisbane-born seamer Alex Cusack, who took two wickets in an over, finished with fine figures of four wickets for 18 runs in his three overs.
But Sri Lanka were already in trouble before he came on.
Former Ireland captain Trent Johnston, also born in Australia, took one for 18 in his four overs while the recalled Boyd Rankin had two for 27.
Tight bowling was backed up by fine fielding, Niall O´Brien setting the tone with three catches and a stumping.
Porterfield got their reply off to a sound start.
The left-hander, who plays for English county Gloucestershire, then cover-drove Kulasekara for well-struck boundaries.
But Niall O´Brien aggravated the right ankle injury he´d sustained in the win over Bangladesh after first slipping and then diving into the crease to make his ground.
O´Brien, who needed several minutes of treatment, then reversed swept Mendis to the boundary and lofted Angelo Mathews for four over long-off.
But a stand of 59 ended in the 10th over when Porterfield was caught behind by Sangakkara off Muttiah Muralitharan.
Earlier Jayawardene, who came in at 14 for two, batted with typical elegance during a 53-ball innings featuring a six and nine fours before he was clean bowled by Cusack.
Ireland took a wicket off only the second ball of the match when the dangerous Tillekaratne Dilshan saw a miscued pull off Rankin held by O´Brien.
The keeper then took an even better catch when, standing up, he held an edge from opposing gloveman Sangakkara off Johnston.
Ireland complete their Super Eights programme against Pakistan at the Oval on Monday while Sri Lanka are in action 24 hours later at Trent Bridge when they face New Zealand.
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