Paceman Mason then removed Matthew Spriegel, Gareth Batty and Stewart Walters in the space of seven balls.
Spinner Gayle bowled Jones and Steve Harmison in the space of three balls to finish the job.
James Hildreth was dropped twice at third slip in the space of three balls and later survived a missed stumping opportunity.
Kent's attempts at a recovery were undermined by the departure of Smith and Andrew Symonds in the space of seven balls.
But a promising stand of 48 was ended by Weeraratne, who dismissed both Misbah and Younus Khan in the space of three balls.
The other two wickets went in the space of three balls to Nantie Hayward and they were the important ones of Sachin Tendulkar and Sourav Ganguly.
The hosts had to recover after a morning session when Ntini struck twice with the new ball before returning ahead of lunch for two more wickets in the space of three balls.
After 10 overs the score had edged up from an overnight 4-0 to 13 when Sami struck, taking out Lou Vincent (four) and Stephen Fleming (nought) in the space of five balls.
Three wickets - including two run-outs - in the space of 12 balls left India 63-4 in the 20th over, but Raj and Roy saw them post what proved to be a winning total.
Needham dismissal of Joshua Cobb before the interval ended a stand of 49 with Paul Nixon after Boeta Dippenaar and HD Ackerman had been dismissed in the space of three balls by Graham Wagg.
Notts then lost their last three wickets in the space of 12 balls as Steven Mullaney was bowled by Patterson with one that kept low and Read was castled by a Shahzad off-cutter, before the England paceman bowled Luke Fletcher with a slower ball.
The Brewers were all over the place, with the home side winning the majority of the loose balls, always probing and looking for space to exploit behind Burton's defence.
I'm used to taking high balls and then trying to get in more space and making the most of that.
Fair Trade Sports sells 70% of its balls online and now aims to get shelf space in Costco and Sports Authority stores.
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