Opting to bat first after winning the toss, RCB began on a brisk pace but lost two quick wickets early on and that put brakes on their scoring rate.
Jadhav then produced an excellent innings as he shifted gears from being watchful to hitting a flurry of big shots to the huge cheers of home supporters at the Chinnaswamy Stadium.
But once Delhi captain Zaheer Khan ended Jadhav's innings in the 17th over, RCB could add just 15 runs off the remaining three overs with Chris Morris picking up two more wickets to restrict RCB to a modest total.
For Delhi, Morris took three wickets for 21 runs while Zaheer grabbed two wickets from 31 as Delhi bowlers produced a disciplined show.
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Watson's choice to bat backfired as RCB lost two quick wickets early on with Chris Gayle and Mandeep Singh getting out cheaply as the home side were reduced to 41 for 2 in the sixth over.
West Indian Gayle, who needed 31 runs to become the first player to score 10,000 runs in T20 cricket before today's match, was dismissed by Morris for just six.
The two early wickets slowed down the pace of scoring but RCB's woes compounded after captain Shane Watson was out stumped off the bowling of Shahbaz Nadeem.
Watson (24 off 24 balls), who was batting cautiously after the two early wickets, was done in by the extra bounce and a bit of turn and he was completely beaten. Rishabh Pant collected the ball outside off and did the rest.
Jadhav continued with a four and six off Carlos Brathwaite to add another 16 in the next over as RCB scored 48 runs in three overs. But once he was out, RCB could not add too many runs.