Chasing a target of 299, the duo hit 65 from 38 balls to leave the tourists needing 10 from the final over. [break]
But Steyn (35) was bowled second ball by Praveen Kumar, while Wayne Parnell (49) was run out chasing three runs for victory off the final ball of the game.
Suresh Raina´s 58 was the highlight of India´s 298-9 from 50 overs.
The match looked destined to end in defeat for the tourists when stand-in captain Jacques Kallis was bowled for 89 in the 43rd over with the score at 225-8.
But a belligerent ninth-wicket partnership between fast bowlers Steyn and Parnell changed the complexion of the match in six brutal overs, plundering a series of heavy blows around the Sawai Mansingh Stadium.
Steyn in particular punished a profligate Sreesanth, who finished with figures of 2-74 from nine overs, smashing three sixes from just 18 deliveries, while partner Parnell batted with intelligence beyond his 20 years in his 47-ball knock.
With his options rapidly depleting, India captain Mahendra Singh Dhoni turned to Kumar in the final over.
And the recently recalled seamer duly delivered as he removed Steyn with a well-disguised slower ball before Parnell was run out from the last ball of the match.
The result ensures that India, fresh from their dramatic innings and 58-run win Test victory in Calcutta earlier in the week which reinforced their top spot in the International Cricket Council´s five-day rankings following a 1-1 series draw, are on course to stay above South Africa in the one-day table.
However, the tourists can still leapfrog their opponents into second place if they win the next two matches in Gwalior and Ahmedabad.
Despite the absence of key players Harbhajan and Yuvraj Singh, Gautam Gambhir and Zaheer Khan, India confirmed their abundant depth of talent just a year out from the World Cup on home soil.
There were recalls for all-rounder Yusuf Pathan, batsmen Dinesh Karthik along with Kumar, while South Africa brought in big-hitting opener Loots Bosman for injured captain Graeme Smith, absent because of a fractured finger.
Temporary skipper Kallis won the toss and inserted India into bat - and was immediately rewarded with the key wicket of Sachin Tendulkar, run out in the second over for four.
Karthik and Virender Sehwag instigated the recovery with a second-wicket partnership of 79, with Sehwag in particular in brutal form.
The dynamic opener smashed six boundaries and two sixes from just 37 deliveries before he was run out for 46 backing up when Charl Langaveldt´s right hand brushed a Karthik straight drive into the stumps at the non-striker´s end.
Karthik (44) departed soon after, while Mahendra Singh Dhoni´s promising innings was cut short at 26 when he drove a caught to Albie Morkel at mid-off to leave the hosts 138-4.
However, Raina, alongside Virat Kohli (31), injected impetus back into India´s innings with a 66-run, fifth-wicket stand, while cameos from Jadeja (22) and Pathan (18) pushed the hosts to 298-9 from their 50 overs.
Kallis was the pick of South Africa´s bowlers, finishing with 3-29 from seven overs.
An aggressive opening stand 58 from just 52 deliveries between the muscular Loots Bosman and Herschelle Gibbs gave the hosts the perfect start as new-ball pair Ashish Nehra and Kumar struggled to contain the free-flowing duo.
Bosman´s innings was curtailed when he bowled backing to the leg-side attempting an overambitious cut shot to Kumar.
Gibbs (27) departed soon after, leaving the imperious Kallis and AB de Villiers to maintain the tempo of the innings.
De Villiers showed glimpses of genius in his 23-ball innings of 25 before he was comprehensively bowled attempting to cut a delivery too close to his stumps.
And India regained momentum when Alviro Petersen (9) failed to ground his bat taking on Sreesanth´s arm, with Morkel falling two overs later, lbw to Nehra.
A rash slog from Kallis saw him fall 11 runs short of a century, but his departure paved the way for an awesome display of late-order pyrotechnics from Parnell and Steyn, setting up one of the most thrilling one-day finish this year.
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