Mandeep Singh (52; 43b 4x4 1x6) also played well to graft the innings after the big three of Chris Gayle, Virat Kohli and AB de Villiers failed to contribute.
Head (75 off 47 not out), who is playing in place of Shane Watson, and Mandeep stitched together a 71-run stand for the fourth wicket to stem RCB's rot and at the end it was about the Australian's big hitting.
While Mandeep took time to steady the ship and pace his innings to perfection, Head saved his shots for the last smashing Ankit Rajpoot and Chris Woakes for two sixes in consecutive overs to up the run rate. In the last over, Head tonked Umesh Yadav (3/36) for two sixes and a four on the trot to take away 21 runs.
Put in to bat, Gayle played a lazy shot first ball of the match for Gambhir to complete the simplest of catches at short cover off Umesh's bowling.
Mandeep looked to take on Chris Woakes, opening the bowling in place of injured Nathan Coulter-Nile, hitting the England pacer for a four and a six off back-to-back deliveries.
Kohli's (5; 9b; 0x4, 0x6) poor form continued unabated as the India captain could not make the most of his reprieve when Piyush Chawla grassed him at mid-off to get out in the very next ball. He fell to Umesh's slower delivery with the ball striking his back foot for a plumb leg before wicket decision.
Sunil Narine sent De Villiers (10; 8b 2x4 0x6) back in his first over with the out of form South African shuffling across the crease to miss the ball completely and losing his stumps as a result.
Mandeep and Head took almost nine overs to engineer a 50-run stand for the fourth wicket. There was a period where RCB could not find the fence for five overs before Head pulled Ankit Rajpoot behind square leg for four.
Play was stopped for around 38 minutes after which Mandeep brought up his half century but the interruption in their partnership saw Narine taking the prized wicket of Mandeep.
Kedar Jadhav holed out to Umesh who ran from long off to pouch the ball to help Chris Woakes grab a wicket. Pawan Negi added just five runs to the total before falling to Umesh in the final over.
Brief scores: Royal Challengers Bangalore -- 158/6 in 20 overs (Travis Head 75 not out, Mandeep Singh 52; Umesh Yadav 3/36, Sunil Narine 2/29) versus Kolkata Knight Riders.
Source - Agency
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