The hosts were agonisingly close to victory, having taken eight wickets in the second innings, but South Africa's tailenders hung on to snatch a draw in the end.
Left-arm spinner Rangana Herath was almost unplayable on a deceptively turning track at the SSC ground, conceding just 40 runs off 45 overs for five wickets.
Off-spinner Dilruwan Perera was also effective, picking 3-60 off 44 overs.
The duo bowled relentlessly, helping Sri Lanka complete 94 overs on the fifth and final day despite several rain interruptions.
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"I'd like to make a special mention about Herath and Perera for the effort that they put in," Mathews told reporters after the game ended.
"They were unbelievable. It was always going to be hard to dismiss (the South Africans) but they put their hearts out to help us win the game. Unfortunately we could not pull it off.
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Mathews said the team was gutted because the draw handed South Africa their first Test series win on the island in 21 years.
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