Rajasthan Royals' hope of making it to the play-off hopes have been crushed as they are out of the tournament, finishing with just 11 points from 14 games.
Rishabh carried on his bat and finished off the chase by hitting Sodhi for a big six over long-leg off and in the process also notched up his fifty. Pant's unbeaten knock was studded with two fours and five hits over the fence.
For DC, veterans Ishant Sharma and Amit Mishra snared three wickets apiece to help Delhi Capitals restrict Rajasthan Royals to 115 for nine.
Ishant (3/38) did the early damage before leg-spinner Mishra (3/17) came to the party to rock Rajasthan's innings.
Young Riyan Parag (50 off 49, 4x4s, 2x6s) was the lone bright spot for Rajasthan as he held on to one fort and notched up his maiden IPL fifty to take the visitors close to the 120-run mark.
Already through to the play-offs, Delhi Capitals first rode on veterans Ishant Sharma and Amit Mishra's superb efforts with the bowl to restrict Rajasthan Royals to 115 for nine and then chased down the target in 16.1 overs, with Rishabh Pant remaining unbeaten on a 38-ball 53.
The win lifted Delhi to the second spot in the standings with 18 points from 14 games but to finish as second best side, the Capitals would need Mumbai Indians to lose against Kolkata Knight Riders on Sunday.
A win for Mumbai would automatically drop Delhi to the third spot as they have an inferior net run-rate.