The tourists, who won the first Test by an innings and 248 runs in Dhaka last week, recovered from 49-2 to a comfortable 314-5 by stumps on the opening day at the Zahur Ahmed Chowdhury stadium.
Left-handed Sangakkara was unbeaten on 160, his 34th Test hundred that drew him level with retired Sunil Gavaskar and Brian Lara in the all-time list of century-makers.
The four above them -- Sachin Tendukar (51 centuries), Jacques Kallis (45), Ricky Ponting (41) and Rahul Dravid (36) -- are also not playing Test cricket.
Sangakkara, a 36-year-old veteran playing his 122nd Test, followed his 75 in the first Test with an impressive innings that has so far contained 19 boundaries and three sixes.
Senior pro Mahela Jayawardene helped close friend and long-time ally Sangakkara put on 178 for the third wicket after Sri Lanka were reduced to 49-2 soon after the first hour.
Jayawardene, who compiled an unbeaten 203 in the Dhaka Test, continued his good form with 72 before being leg-before to off-