Jayasuriya hit an 88-ball 130 and Sangakkara notched 121 for his third century in the tournament as the duo punished a hapless Bangladesh during their 201-run opening stand in the Super League match at National Stadium.
Jayasuriya was ruthless from the outset, hitting shots with power and precision. He took just 31 balls to reach his half-century.
He continued in the same vein to reach his 26th one-day hundred off 55 balls -- the sixth-fastest hundred in one-day cricket -- with 14 boundaries and five sixes.
Jayasuriya becomes the second oldest batsman to score a one-day hundred behind England's Geoff Boycott who made a century against Australia at Sydney in 1979 when he was 39 years and 51 days old.
Jayasuriya miscued a drive off leg-spinner Alok Kapali and was caught in the 28th over. In all he hit 16 boundaries and six sixes during his devastating knock.
Sangakkara was steadier as he batted around Jayasuriya and took runs whenever he got the opportunity. He reached his hundred off 117 balls before he was bowled by left-arm spinner Abdur Razzak in the 44th over.
The 30-year-old left-hander hit 16 boundaries and a six off 128 balls.
Sri Lanka beat Pakistan by 64 runs in the opening match of the Super League on Sunday. India, the fourth team in the second round, beat Bangladesh on Saturday.
The top two teams from the Super League will compete in the July 6 final.