The 22-year-old de Kock continued his purple patch in ODIs against India, scoring his fourth century in seven innings against the opponents to set up South Africa's total of 270-7 in 50 overs after they chose to bat on winning the toss.
The hosts lost opener Shikhar Dhawan (13) early to Morkel but looked well poised for a victory charge with half-centuries from Rohit Sharma (65) and Virat Kohli (77).
Opening batsman Rohit and Kohli added 72 for the second wicket before the former fell to a smart return catch from part-time off-spinner JP Duminy.
Kohli then added 80 for the next wicket with his captain Mahendra Singh Dhoni (47) to keep India in the hunt before Morkel returned to strike.
The South African plan of bowling short at the batsmen's bodies while packing the leg side boundary with four fielders proved effective.
After Dhoni failed to negotiate a short delivery from the tall Morkel, Kohli and Ajinkya Rahane holed out deep on the mid-wicket fence on consecutive deliveries in the paceman's final over, which put paid to India's hopes of chasing down the total.
India could only manage 252 for six in their 50 overs.
Earlier, South Africa sent David Miller, who had scored 13 and nought in the series, to open the innings to help him regain form and the new opening pair gave the touring side the ideal start with a stand of 72.
India off-spinner Harbhajan Singh and leg-spinner Amit Mishra stemmed the flow of runs while bowling in tandem and gave away 79 runs between themselves in their 20 overs, picking up a wicket each.
De Kock, who hit 11 fours and a six in his knock, added another 118 for the third wicket with Faf du Plessis (60) to set up a solid platform for South Africa for a late assault.
Du Plessis lived a charmed life on his way to his third consecutive 50 in the series. Suresh Raina and Dhawan dropped him twice while the right-hander was also caught when on 16 but replays showed Mohit Sharma's delivery was a no-ball.
His dismissal to Mohit sparked a mini-collapse and South Africa were suddenly reduced from 205-2 to 210-5 in the space of nine deliveries.
South Africa captain Ab de Villiers and de Kock, who was run out by a direct throw from Dhawan, were the two other batsmen out during that period which robbed South Africa of momentum.
The fourth match will be played in Chennai on Thursday.
(Reporting by Sudipto Ganguly; editing by Alan Baldwin)
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