Dhawan's unbeaten 31 came off 71 balls with the help of four boundaries, while Cheteshwar Pujara, batting on 14 off 29 balls, hit the only six of the session so far.
For South Africa, off-spinner Dane Piedt, playing his first Test of the series, removed in-form Murali Vijay for 12.
This was the fourth time in the series when skipper Virat Kohli won the toss and immediately opted to make first use of the Kotla track.
It was in the 13th over that Dhawan drove off-spinner Piedt through wide of mid-on for the first boundary. In the next over bowled by Abbott, the left-hander pushed one firmly through the extra cover region to collect his second boundary.
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Vijay was lucky to get a reprieve on personal score of 10 when Kyle Abbott delivery, which saw him edge one to AB de Villiers at second slip, was rightly ruled 'no-ball' by the third umpire CK Nandan.
After being hit in the stomach region by an incoming delivery from Abbott, the Tamil Nadu opener uncharacteristically pushed a straighter one from Piedt to find Hashim Amla pouch one at the first slip. His 84-minute stay yielded only 12 runs as the first wicket fell at 30.
Dhawan continued to play his shots as he square drove Morkel in his second spell for his third boundary.
Cheteshwar Pujara's first assertive shot was a deliberate glide past Amla at first slip off Piedt's bowling to get his first boundary. The 50 came in the 25th over.
Pujara also grew in confidence as Imran Tahir's loopy full toss was dispatched disdainfully over deep mid-wicket for the first six of the match.