Kemp made 100 not out off 89 balls as South Africa reached 274 for seven after winning the toss on Sunday.
It was a total which seemed unlikely after Indian left-arm opening bowler Zaheer Khan plunged the innings into disarray.
Khan took two wickets for no runs in the first over and had an opening spell of three for nine off seven overs.
South Africa slumped to 76 for six before Kemp and Shaun Pollock (33) put on 60 for the seventh wicket.
Even then, South Africa were in a shaky position but Kemp and Andrew Hall (56 not out) put on a South African record 138 in an unbeaten partnership for the eighth wicket with some audacious strokeplay. They scored their runs off only 92 balls.
The tall Kemp, who survived difficult chances on nine and 35, hit seven sixes and six fours. His first 50 runs were scored off a relatively sedate 67 balls as he and Pollock rebuilt the innings but he went on the rampage to score his second half-century off 22 deliveries.
Khan was among the bowlers who suffered as South Africa hammered 113 off the last ten overs, including 77 off the last six.
Khan finished with three for 42 after seemingly putting his side on target to level the series, which South Africa lead 1-0 after the first match was rained out.
Khan was on target from the start of the match, with Graeme Smith surviving an appeal for leg before wicket off the first ball only to be bowled by the next delivery when he failed to get forward to a ball which angled in to beat the South African captain.
Two balls later, Jacques Kallis, who made a century to set up South Africa's 157-run win in Durban Wednesday, drove loosely outside the off stump and was caught by Sachin Tendulkar at first slip.
Khan claimed a third wicket when Loots Bosman, who took 20 balls to score his first run, was out in similar fashion to Kallis, caught at first slip by Tendulkar for six.
Herschelle Gbbs and AB de Villiers batted brightly for 35 and 29 respectively but when Pollock was the second of two run-out victims India were on top before the Kemp-Hall partnership.
Hall had not been due to play but was a late replacement for Andre Nel, who was said by team management to have a finger injury. He made his 56 off 47 balls with seven fours.
India made four changes. Fast bowler Munaf Patel was ruled out with an injured ankle but opening batsman Virender Sehwag returned after missing the Durban match because of a finger injury.
Dinesh Karthik, Irfan Pathan and veteran leg-spinner Anil Kumble were selected ahead of Wassim Jaffer, Suresh Raina and Dinesh Mongia.