India were 153 for no wicket at tea Tuesday, with Jaffer unbeaten on 84 and Karthik on 63.
India's previous best opening stand in the series was 20, with both Jaffer and Virender Sehwag struggling against South Africa's fast bowlers.
The selectors persevered with Jaffer after he showed promise with innings of 26 and 28 in the second Test in Durban. The hard-hitting Sehwag was retained despite scoring only 45 runs in four innings but it was decided he would move down the order.
Wicketkeeper Karthik came into the side after Mahendra Singh Dhoni was ruled out because of an injured right middle finger and was promoted to opening batsman.
Karthik gave a chance on 32 when South African captain Graeme Smith could not hold a low edge at slip off Shaun Pollock. He also mistimed a drive just short of Herschelle Gibbs at cover off left-arm spinner Paul Harris when he had 53.
But there was hardly any other encouragement for the bowlers on a placid pitch after Indian captain Rahul Dravid won the toss and decided to bat.
Jaffer was the senior partner, striking some firm drives and neat clips off his toes, while Karthik was content to leave the ball alone as much as possible early in his innings before playing some more expansive strokes after lunch.
Jaffer reached his fifty off 114 balls, while Karthik needed 144 deliveries to reach the mark.
Although there had been expected to be early life in the pitch, the South African bowlers seldom troubled the Indian batsmen, who both played each ball on its merits.
With the pace bowlers unable to make a breakthrough, left-arm spinner Paul Harris had three overs before lunch in his debut Test, bowling steadily and conceding seven runs.
India 153/0 (Wasim Jaffer 84 n o, Dinesh Karthik 63 n o) Vs South Africa