Pecker is a key witness in the case against the former US president, who is accused of falsifying business records to cover up hush-money payment
In a must-win match for the hosts, Bangalore, who went in with an unchanged side, posted 218 - thanks to some big hitting from AB de Villiers, Moeen Ali, Colin de Grandhomme and tailender Sarfaraz Khan.
Their bowlers then struggled against Hyderabad but managed to curtail them to 204 for 3 after Hyderabad captain Kane Williamson (81 from 42 balls, 7x4, 5x6) and Manish Pandey (62 not out, 7x4, 2x6) had threatened to take the match away from Bangalore at one stage with a 135-run partnership.
Earlier, put into bat, De Villiers (69 from 39 balls; 12x4, 1x6) and Moeen (65 from 34; 2x4, 6x6) put on a 107-run third wicket stand to resurrect RCB's innings which fell apart after the early loss of the opening duo of Parthiv Patel (1) and skipper Virat Kohli (12).
Put in to bat, Parthiv failed to take advantage of the dropped chance off the very first ball and departed off the final ball off Sandeep Sharma, caught by Siddharth Kaul at third man.
Kohli followed his opening partner soon after adding 32 runs with de Villiers, as the India skipper's struggle with the spinners continued in this edition of the IPL. The right-hander attempted to slog Rashid Khan's fuller length delivery hoping for a googly only to find his stumps re-arranged.
Struggling at 32 for 2, de Villiers and Moeen changed the complexion of the innings in no time, with both batsmen trying to outscore each other as it started raining boundaries at the Chinnaswamy Stadium.
De Villiers started with two consecutive boundaries off Shakib Al Hasan before sending the other Hyderabad bowlers on a leather hunt, before Moeen joined the party by welcoming rookie pacer Basil Thampi, who replaced Bhuneshwar Kumar, with two consecutive sixes.
Thampi proved to be the most expensive bowler in IPL history when his figures showed 4-0-70-0.
In no time, the South African veteran brought up his half century in mere 32 balls, when he pulled medium pacer Kaul for a boundary before Moeen, who was dropped on 23 by Shikhar Dhawan off Sandeep, turned on the heat by meting out some special treatment to Thampi.
The English southpaw mercilessly smacked Thampi for a boundary to bring up his maiden IPL half century off just 25 balls before Afghan leg-spinner Rashid came back to break the partnership in a span of three balls.
Rashid first saw the back of de Villiers brilliantly caught by Dhawan at deep backward square before packing Moeen one ball later, caught behind by Shreevats Goswami.
With both the set batsmen back in the dugout, the visitors sniffed at a smaller total when they packed an in-form Mandeep Singh (4) cheaply.
But New Zealander Colin de Grandhomme (40 from 17; 4x1, 6x4) and teenaged Sarfaraz Khan (22 not out from 8; 4x3, 6x1) lit up the stadium with some late order fireworks, to ensure the home side crossed the 200-run mark with a quick-fire 34-run stand.
For the tourists, Rashid once again emerged the pick of the bowlers with figures of 3/27, while Siddharth and Sandeep chipped in with two and one wickets, respectively.
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