Meanwhile, Kohli looked relaxed ahead of the must-win game as he went out for dinner with teammates in his home city.
But the jubilant Delhi crowd soon fell silent as Kohli and de Villiers took over.
The last 29 balls fetched 61 runs for Delhi with Sharma and Vijay Shankar (21 off 20) sharing an unbeaten 61-run stand off 30 balls.
RCB's chase didn't get to the best of starts. Abhishek, who was an important part of India's Under-19 World Cup-winning team in New Zealand earlier this year, hit three fours and four sixes during the course of his innings.
The game also saw the debut of young spinner Sandeep Lamichhane, the first cricket from Nepal to feature in the IPL.
Delhi suffered their first blow in the opening over itself when opener Prithvi Shaw was bowled while attempting a rather languid shot off Chahal's bowling.
Facing an imposing target, RCB lost both their openers inside three overs.
Pant's dismissal also ended his partnership of 93 off 62 with captain Shreyas Iyer. Yuzvendra Chahal picked up the wickets of Prithwi Shaw and Jason Roy to leave Delhi at 16-2 in the powerplay.
Pant played a major role in boosting the run rate.
Off-spinner Moeen Ali finally brought the rampage to an end when Pant attempted another big hit, only to be caught by de Villiers near the boundary rope wide of long-on.
At the other end, de Villiers was sedate to begin with, but got into his stride when he welcomed Amit Mishra into the attack with a huge six over long on.
The RCB captain marred Daredevils' third debutant Junior Dala's hopes of a good IPL start as he greeted the South African with two fours and a six in the fourth over. The ball was a full-toss and way outside off-stump and de Villiers shuffled across to take the unorthodox sweep shot over the backward square leg.
While Kohli walked back after scoring 40-ball 70, De Villiers took the onus to finish things up and cross the victory line. Meanwhile, Harshal Patel gives away 19 runs from this over.
Earlier, RCB's bowlers began well with early scalps, but Pant and Abhishek wrested the momentum DD's way and led the side to a competitive total.
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