The veteran left-hander’s 16th one-day century steered Sri Lanka to a commanding 320-5 after the hosts were sent in to bat in the day-night game at the Premadasa stadium.
South Africa were shot out for 140 in reply, the innings lasting just 31.5 overs, to leave Sri Lanka with a 1-0 lead in the five-match series.
Thirty-five-year-old Sangakkara chippped in with two catches and a stumping, earning him the man of the match award, as Rangana Herath and Thisara Perera picked up three wickets each.
Sangakkara celebrated his 350th one-day match by surpassing his previous best score of 138 not out, against India in 2005, after Tillakaratne Dilshan fell cheaply in the fourth over.
Sangakkara put on 70 for the second wicket with opener Upul Tharanga (43), 74 for the third with Mahela Jayawardene (42) and 123 for the fourth in which Lahiru Thirimanne’s contribution was just 17.
He finally holed out in the deep in the penultimate over of the innings, after 18 boundaries and six sixes.
Fast bowler Morne Morkel, who recovered in time from a thigh injury to play the match, was South Africa’s most impressive bowler with 2-34 from his 10 overs.
But the inexperience of the depleted touring squad told in the end as the Sri Lankans batted fluently and bowled a steady line on the slow pitch.
South Africa are without three frontline players — fast bowler Dale Steyn, all-rounder Jacques Kallis and former captain Graeme Smith — for the tour which also includes three Twenty20 matches.
The tourists also missed premier batsman Hashim Amla, who was unavailable for the first match due to a strained neck.
South Africa made the worst possible start when Colin Ingram was bowled off the first ball of the innings by sling-arm fast bowler Lasith Malinga.
Skipper AB de Villiers and Alviro Petersen added 44 for the third wicket to lift the total to 73-2 when both batsmen fell in successive overs.
Wickets continued to tumble at regular intervals, leaving Petersen and Robin Peterson as the top-scorers with 29 each.
The second match will be played at the same venue on Tuesday.