Karthik's 51 came from just 45 balls and he was dismissed by 19-year-old Yorkshire leg-spinner Adil Rashid.
Muralitharan then snapped up the wickets of Gambhir (43), Sourav Ganguly, Dinesh Karthik and Anil Kumble.
Dinesh Karthik and Parthiv Patel will compete for vice-captain Dhoni's place behind the stumps.
Haq was rewarded for some tidy slow bowling when Dinesh Karthik was well caught at mid-wicket.
Dinesh Karthik is only 19, and had not played a senior international until today.
Indian opener Dinesh Karthik struck 51 in India's second innings of 91-1 before the game was declared a draw.
Dinesh Karthik, Mahendra Dhoni and VVS Laxman were all dismissed cheaply for the second time in the game.
Lieberman's students Birago Jones and Karthik Dinakar are working on an algorithm that would automatically detect bullying language.
Dinesh Karthik, also challenging for a Test place, made a composed 76 before he fell in the final over before tea.
Rahul Dravid got going with a sweetly-time on-drive for four but Karthik (22) was not able to join him at the moment of victory.
Virat Kohli, who was rushed out to take Yuvraj's place for the Champions Trophy, retains his place in the side ahead of wicketkeeper-batsman Dinesh Karthik.
Starting the final day on 10-0 needing just 73 to win the second Test, India were cruising before Tremlett dismissed Wasim Jaffer and Dinesh Karthik.
Karthik reached his half-century in fine style by driving James Kirtley for four, and twice dispatched him off the back foot to the square cover boundary.
Jaffer took a boundary off Ryan Sidebottom, Karthik crashed Anderson to the point fence again and India looked well on the way to a 10-wicket victory.
Karthik Naralasetty, 22, had been navigating his way through Rutgers University when he ran out of money for college and had to move back to India.
FORBES: A New Generation of Techonomists Are Driven To Change the World
Karthik shared 129 in 41 overs with left-hander Gautam Gambhir who made 81, and skipper Rahul Dravid and VVS Laxman added a quickfire 75 in 19 overs.
Then came the first of the run outs, with Pietersen calling Collingwood for a suicidal single having hit straight to substitute fielder Dinesh Karthik at short cover.
Klusener was the first to go, caught off the bowling of rookie spinner Murali Karthik for 97, followed by Kallis caught by Wasim Jaffer off Anil Kumble for 95.
Sehwag's 66 off 42 deliveries, followed by Karthik's 61 off 41 deliveries - including three consecutive sixes off Ajantha Mendis - helped their side to a total of 170-5.
Rahul Dravid had placed a leg slip specifically for the leg glance, and his plan should have worked perfectly but Dinesh Karthik spilled the chance after juggling with the ball.
Vineet, Eden, Karthik, and Vivek are part of what may be the most civic-minded and socially conscious generation yet, and their use of technology is integral to driving their projects.
FORBES: A New Generation of Techonomists Are Driven To Change the World
Two researchers, Karthik Muralidharan of the University of California at San Diego and Venkatesh Sundararaman of the World Bank, tested that idea in 300 state-run schools in Andhra Pradesh in India.
Yuvraj Singh (25) was caught at cover off the bowling of Shahadat Hossain and Dinesh Karthik (27) went when Rubel Hussein took a diving catch at mid-off, giving off-spinner Mahmudullah his second scalp.
Ravindra Jadeja (20), Virender Sehwag (19) and Dinesh Karthik (14) were the only batsmen to reach double-figures in India's dismal batting performance, with fast bowlers Mills and Jacob Oram bagging two wickets each.
Former Pakistan Test off-spinner Saqlain Mushtaq, whose British passport arrived on Monday, was making his first-class debut for Sussex and bowled Karthik through the gate with one that turned in as he pushed forward.
As soon as Karthik square cut James Anderson to the boundary in the first over from the Radcliffe Road End it was clear there was unlikely to be a serious challenge to India's victory parade.
In the second game on Sunday, Virender Sehwag and Dinesh Karthik both hit half-centuries as the Delhi Daredevils claimed a a 50-run win over Sri Lanka's Wayamba to keep their hopes of winning the trophy alive.
Rubel Hossain took a simple catch from a Shakib full-toss to claim the wicket of Yuvraj Singh (12), and stand-in captain Dinesh Karthik (0) was smartly snapped up by Raqibul Hasan to become Shahadat's third victim.
BBC: Tendulkar sets record as Bangladesh make India struggle
Dinesh Karthik steered his second ball to extra-cover to give Stuart Broad a wicket but Dravid responded stylishly to the mini-crisis, cracking three boundaries in an over from Broad as he got to 50 off 51 balls.
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