Elgar, 27, hit nine fours and a six in his 91-ball knock after new Test skipper Hashim Amla chose to bat on a placid track at the Galle International Stadium.
The left-handed Elgar and his partner Alviro Petersen (34) gave the visitors a steady start, putting on 70 for the opening wicket off 101 balls.
Petersen was particularly severe on left-arm spinner Rangana Herath, welcoming him with four boundaries in his first over of the day.
The opener, playing in his 10th Test, reached his second half-century in style, smashing off-spinner Dilruwan Perera through midwicket for an elegant boundary.
He also lofted Perera over the long-on boundary fence for the only six of the session.
Desperate for a breakthrough, Sri Lankan skipper Angelo Mathews made frequent bowling changes but failed to find success until the 17th over, when Perera (1-31) had Petersen trapped leg before wicket.
Petersen was unhappy with the decision of on-field umpire Richard Kettleborough and asked for a review.
Faf du Plessis, batting at number three for the first time, was unbeaten on 14 at the break.
Earlier, South Africa picked a lone specialist spinner in Imran Tahir with JP Duminy as a part-time off-spinner.
Sri Lanka close two slow bowlers in Herath and Perera.
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