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 pl