Kolkata were tottering at 45-6 chasing a modest 102-run target before Shukla steered his team home with a 57-run stand for the unfinished seventh wicket with Ajit Agarkar (13 not out).
Man-of-the-match Shukla smashed two sixes and three fours in his 46-ball knock.
Shane Warne´s Rajasthan failed to qualify for the semi-finals, finishing their league engagements with 13 points from 14 matches. Kolkata finished last with seven points.
Delhi lead the eight-team tournament with 18 points from 13 games, followed by Chennai (15/13), Deccan (14/13), Bangalore (14/13), Punjab (14/13), Rajasthan (13/14), Mumbai (11/13) and Kolkata (7/14).
The top four sides advance to the semi-finals.
South African fast bowler Charl Langeveldt earlier played a key role in restricting Rajasthan to a small total, finishing with 3-15 off four overs in his only match of the tournament.
He was backed by Indian seamer Agarkar, who grabbed two wickets for 15 runs in four overs.
Naman Ojha top-scored for Rajasthan with 22.
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