Dale Steyn grabbed a match haul of 9-99 as South Africa won the first Test by 153 runs on the fifth and final day in Galle on Sunday.
South Africa, currently the world No.2, can reclaim the top world ranking from Australia if they win the second and final Test in Colombo from July 24-28.
Steyn’s figures, the best by a quick at the Galle ground, helped the visitors bowl Sri Lanka out twice despite a wicket which offered little help.
It was only South Africa’s third win on the island and their first since 2000.
Steyn was well supported by seamer Morne Morkel, who picked up four wickets as Sri Lanka’s second innings ended on 216 shortly into the second session.
The hosts needed to make another 260 runs on the final day with nine wickets in hand to pull off a come-from-behind win. But they lost their remaining wickets for just 106 to go down tamely.
South Africa made 9(dec)-455 in their first innings before bowling out the home side for 292. In their second knock, South Africa declared at 6-206 to set Sri Lanka a target of 370.
The victory was especially sweet for Hashim Amla, who was leading the side for the first time in Test cricket.
Part-time spinner Jean-Paul Duminy picked up two wickets including the crucial scalp of Kumar Sangakkara, who made a fighting 76 to salvage some pride for the hosts.
Sri Lanka, who had resumed on their overnight 1-110, added just 51 off 24 overs in the first session while losing five wickets.
“South Africans outplayed us on all the five days,” said Sri Lankan skipper Angelo Mathews.
“We don’t mind losing games if we have played good cricket but in this game we were really disappointing.”
Steyn, who had taken a five-wicket haul in the first innings, struck in the fourth over of the day to give his side the breakthrough they needed.
His victim was opener Kaushal Silva (38) who nicked the seamer behind the wickets, where Quinton de Kock dived to his right to take a stunning catch.
Silva’s dismissal ended a 104-run stand with Sangakkara for the second wicket, the highest of the innings.
Sri Lanka were dealt a bigger blow off the first ball after the drinks break when Morkel had Mahela Jayawardene caught behind for 10.
Sangakkara was dropped on 65 but failed to take advantage of the reprieve, pulling Duminy to short midwicket where Amla took a fine catch.
He hit nine fours and a six in his 145-ball innings.
The dismissal of Sangakkara and Jayawardene in quick succession infused new energy into the visitors, who quickly wrapped up the victory.