The Bangalore top order batsmen, except for Rahul (68 not out), failed to click after being put into bat but a late flurry of lusty blows from the wicketkeeper batsman saw the home side reach to a fighting total at Chinnasawmy Stadium.
Rahul, who came in when Bangalore were in a precarious 17 for two in the fourth over, struck three fours and four sixes in his 53-ball unbeaten innings.
Bangalore were 60 for 2 at the halfway stage but added 91 runs from the next 10 overs. Sachin gave an able support to Rahul towards the close of the innings with a quickfire knock of 13-ball 25 not out which had two fours and two sixes.
The cause of the home side was helped by the 23 runs Kieron Pollard leaked in the 18th over with Sachin Baby hitting two sixes and a four while Rahul also his share of a maximum hit.
Bangalore captain Virat Kohli (7), who has been in red hot form, met with a rare failure of the season. He struck a six in the fifth ball of the match bowled by Southee but was dismissed in the second over by Mitchell McClenaghan.
Kohli poked at a shortish delivery which was angling away, trying to guide it to third man, but only to find Harbhajan Singh taking an easy catch.
Two overs later, Chris Gayle (5) perished as he tried to smash a back of a length delivery on the off bowled by Southee with Rohit Sharma taking a well-judged catch.
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