The left-hander made 130 not out as Sri Lanka, faced with a world record target of 492, defied the Pakistani bowlers to finish with 391-4 on the fifth day at the Sinhalese sports club.
Rock solid Sangakarra's 19th Test century featured a fourth-wicket stand of 122 with Thilan Samaraweera (73) and 114 for the unbroken fifth with Angelo Mathews (64 not out).
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Sri Lanka clinched the series 2-0, their first at home against Pakistan after five unsuccessful attempts, and provided Sangakkara with a winning start as captain after he took over from Mahela Jayawardene in April.
Sangakkara hung on for nearly seven hours on a placid pitch to frustrate Pakistan's bid to record a face-saving win ahead of the five-match one-day series starting at Dambulla on July 30.
No team has achieved this high a target in the fourth innings to win a Test match. The highest successful chase so far is 418-7 by the West Indies against Australia in Antigua in 2003.
The two teams went into the last sessio