The home side failed to find the momentum against the RCB bowlers, who stuck to a perfect line and length as the last five overs yielded just 46 runs for the home side.
Put into bat, Ajinkya Rahane's (6) dismal run continued to haunt Pune before opener Rahul Tripathi (37) cashed in on the dropped chance by Virat Kohli at 11, to help the hosts cross the 50-run mark with skipper Steven Smith (45).
RCB made up for the dropped chance of Tripathi off pacer Adam Milne, when Rahane's attempt to sweep a full delivery from Samuel Badree resulted in a top edge to Milne at short fine leg.
In walked Smith, who looked in good touch and together with Tripathi raised a 40-run second wicket stand before the Maharashtra right-hander spoilt another good start to be caught behind by Kedar Jadhav off left-arm spinner Pawan Negi.
The fall of Tripathi, who slammed four boundaries and a six during his 28-ball knock, however dried up the boundaries for Pune before Smith broke the shackles in the 12th over, by spanking Badree for a flat six and two consecutive fours.
New man Manoj Tiwary (44 not out), promoted to No.4 joined the party by taking Yuzvendra Chahal to the cleaners before Smith added two more fours off Stuart Binny as the third wicket partnership flourished to 50 off 32 balls.
Binny, however avenged the thrashing on the fifth ball of his over when Smith, after facing 32 balls and striking five fours and a six, skewed a slower one high in the air for Milne to take it clumsily at long leg.
Struggling to find the momentum at 115/3 after 16 overs, Pune needed Mahendra Singh Dhoni (21 not out) and Tiwary to press on the accelerator and the former skipper responded in style by muscling Sreenath Aravind for a flat straight six.
But Kohli's ploy to continue with Milne and Aravind at the death paid rich dividends as the duo gave little room for Dhoni and Tiwary to free their arms towards the end.
Brief Scores: Rising Pune Supergiant 157/3 (Steve Smith 45, Manoj Tiwary 44 not out, Rahul Tripathi 37, Stuart Binny 1/17, Pawan Negi 1/18) vs Royal Challengers Bangalore.
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