He also became the first batsman to score hundreds in three consecutive World Cup matches.
Sangakkara was 39 short of reaching the milestone when he came out to bat at the Sydney Cricket Ground. Chasing a mammoth 377-run target, Sangakkara put up a spirited show with his fluent century and kept Sri Lanka in the hunt till he was dismissed.
Left-hander Sangakkara, 37, got to the feat with a paddled two to fine leg off spinner Glenn Maxwell in the 14th over of Sri Lankan innings.
Sangakkara has been in prolific touch and in his last two outings scored back to back centuries.
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He scored a 73-ball ton against Bangladesh and then notched up another impressive hundred off 70 balls against England.
Both his hundreds proved to be match winning ones and gave Sri Lanka much needed fillip after their poor start against New Zealand in the tournament opener.
The retired Tendulkar remains way in front with 18,246 runs in 463 matches.
The three centuries took Sangakkara's tally to 24 hundreds and he has the most centuries for Sri Lanka after Sanath Jayasuriya's 28 tons.
Sangakkara also became the first Sri Lankan batsman to notch up 14,000 runs in ODIs.