Jayasuriya celebrated his 39th birthday with an 88-ball 130 while Sangakkara scored 121 to help Sri Lanka pile up a mammoth 332-8 before Muttiah Muralitharan took 5-31 to bowl Bangladesh out for 174 in 38.3 overs.
Sri Lanka beat Pakistan by 64 runs in the opening match of the Super League on Sunday. They have six points after winning two matches and carrying over two points on account of their win over Bangladesh in the first round.
India, who beat Bangladesh on Saturday, also have four points. They come face to face with Pakistan in a crucial match on Wednesday. If they win, India will meet Sri Lanka for a repeat of the 2004 final, here on July 6.
The match was a one-sided affair after Sri Lankan captain Mahela Jayawardene won the toss and opted to bat, with the innings built around a massive 201-run partnership for the opening wicket between Jayasuriya and Sangakkara in 169 balls.
Jayawardene was full of praise for the two centurions.
"Both Sanath and Sangakkara played well and ensured we made a solid total. It was disappointing to lose wickets in the middle order but then Muralitharan bowled very well to help us qualify for the final," said Jayawardene.
Bangladesh failed to match the strokeplay of the two left-handed Sri Lankans. Only Raqibul Hasan (52) and opener Nazimuddin (47) offered resistance in an otherwise listless batting display.
Nazimuddin was run out after hitting seven boundaries and a six during his 59-ball innings, while Hasan smashed seven boundaries during his 63-ball knock before Muralitharan had him caught by Jayawardene.
Bangladesh coach Jamie Siddons admitted the Sri Lankans were too good for his young team.
"They were too good for us on the day. It was a big target and Muralitharan was too hot to handle," said Siddons of the Sri Lankan wizard.
It was Muralitharan's ninth five-wicket haul in limited overs cricket.
Earlier, Jayasuriya and Sangakkara punished the hapless Bangladesh attack.
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 internationals -- with 14 boundaries and five sixes.
Jayasuriya becomes the second oldest batsman to score a one-day hundred behind England's Geoff Boycott, who scored 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 had 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 lost their last eight wickets for just 99 runs. Alok Kapali and Reza took two wickets apiece.