Chasing 158 for a win on a Chinnaswamy Stadium pitch which was good for batting, Delhi messed up in their chase as they ended at 142 for 9. Young Rishabh Pant's 36-ball 57 which was studded with three fours and four sixes went in vain.
Delhi lost wickets at regular intervals in the light of some tight bowling from RCB and none of their specialist batsmen did stay for long to give company to Pant. The shot selection of most of Delhi batsmen left a lot to be desired.
Pawan Negi did the trick as he took two wickets in the final over, including that of Pant to end the Delhi innings.
Delhi made a steady start in their run chase with Sam Billings and Aditya Tare getting the runs without taking too many risks. But RCB bowlers struck two quick wickets in the space of six deliveries to bring their side into the match.
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Then, Karun Nair (4), who recently played against Australia in the Test series, lasted for just three balls as he was clean-bowled by a gem of a delivery from Stanlake which went through his defences and hit the off-stump.
Billings hit a six off a reverse sweep in the seventh over bowled by Yuzvender Chahal but fell in the next over off Iqbal Abdulla as Delhi were reduced to 55 for 3.
Delhi reached 79 for 3 at the halfway mark, needing another 79 from the remaining 10 overs. Sanju Samson's shot selection was left a lot to be desired as he fell in the 11th over and Delhi found themselves in trouble.
It was anybody's game still with Delhi needing 37 from the final four overs. Watson conceded just five runs and also got the wicket of Pat Cummins (6) in the 17th over to tilt the game in favour of RCB.
In a tense tussle, Pant hit a six off Tymal Mills but Delhi still needed 21 from the final two overs. Amit Mishra consumed a lot of deliveries and that piled pressure on Pant who was out in the final over to end Delhi's hopes.
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.
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.
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 sixth over. 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.