The win by 285 runs lifts them out of the relegation zone in Division One of the County Championship after a tricky start to their first season back in the top flight in nine years.
In the previous game at Canterbury Kent had been humiliated by leaders Somerset, losing by 10 wickets after being skittled for just 59 in the second innings.
But thanks to centuries from former Tonbridge School pupil ZaK Crawley and Joe Denly, and five-wicket hauls for Matt Milnes and Harry Podmore, they eased to victory on the fourth afternoon in Tunbridge Wells.
A burgeoning relationship between pace bowlers Milnes and Podmore is starting to reap results on the field for the young new-ball partners.
Milnes, who joined Kent from Nottinghamshire in the close season, and Podmore, now in his second season having switched from Middlesex, have taken almost 70 Championship wickets between them this summer.
At the Nevill the 24-year-old Milnes took 5 for 64 against his old club for a maiden first-class five-wicket haul, while Podmore grabbed 5 for 41 in the second innings, including a crucial opening burst of that sparked Kent’s drive for victory.
They have already become firm friends off the field and, according to Podmore, they are enjoying each other’s success on it.
“Matt came to live with me in the same flat when he arrived at Kent and we’ve got on really well right from the start,” said Podmore.
“I’ve obviously not known him for that long but we’re like best mates already,and he’s a top professional in the way he trains and works at his game as well as being a top bloke.
“That’s why I was so chuffed for him during Nottinghamshire’s first innings when he got his maiden first-class five-wicket haul.
“It was particularly special that he did it against his old county. I knew exactly how he felt when he got that fifth wicket because my own first five-for in Championship cricket was against my old club Middlesex last season.
“Matt and me are the same age – there’s only a few days between us actually – and we both turn 25 next month (July) and so I reckon we can be a bowling partnership for a lot of years to come if we keep improving and working hard.”
Podmore added: “I think we complement each other in style, and we’re both so happy to see the other succeed.
“I think the fact we’re best mates helps to drive us on, because we can support each other both on and off the field.”
Kent’s next game is against Warwickshire at Canterbury on Sunday [June 30].
Quotes from Mark Pennell, ECB Reporters Network