Had Steve McQueen suddenly appeared on a motorbike and attempted to clear the Eric Hollies stand, the sense that a great escape was in progress could hardly have been more clear.

Well, that's how it seemed for an hour or two anyway.

When Henry Brookes walked out to join Tim Ambrose, Warwickshire were 121 for 7 in their second innings and still required 37 more to make Kent bat again. Victory with two sessions unused seemed likely.

Over the next three or so hours, though, the pair added 144 in 45 overs. Ambrose registered his highest first-class score since 2015 and Brookes the highest of his fledging career, with both demonstrating the benefits of playing straight and not chasing or following the ball.

And, as the Kent bowlers started to flag - the decision to enforce the follow-on sentenced them to 213.1 successive overs in the field; if anyone sees Mitchell Claydon standing on public transport in the next few days, you really should offer him your seat - so Warwickshire's hopes started to rise. First the pair ensured Kent would have to bat again, then that they would have to chase 50 and, with tea approaching, they took the target required above 100 with the overs-remaining equation starting to become relevant.

There's nothing new about Ambrose's batting. He continues to score heavily with the cut and here, forced by the match situation to play straighter and with more discipline than is always the case, he defended solidly. This was the 18th first-class century of an excellent career.

Brookes is at the start of his career. And while 19-year-olds don't come with guarantees, he surely has all it takes to achieve fine things in the game. It is his fast bowling that really excites, but he showed here a welcome ability not just to bat but to rise to the occasion and perform under pressure. While the first few boundaries were generally deflections into the leg side, as he settled he produced some fine cuts and a booming straight drive.

But all that resistance was to come to nothing. When Matt Milnes returned with the newish ball he eventually trapped Ambrose, playing slightly across the line, with a delivery that nipped back and may have kept a fraction low. Within moments, the admirably nagging Harry Podmore dismissed Jeetan Patel in similar fashion - Patel planted his front foot and missed one - before Brookes attempted to whip one into the leg side. The last three wickets had fallen for just 15 runs and, on a fine surface, only two men in the top eight had made double-figures.

Perhaps, on another pitch, Warwickshire may have fancied themselves to have a chance of defending the target of 123 in a minimum of 32 overs. Certainly Ryan Sidebottom and Brookes worked up some impressive pace at the start of the reply, but Warwickshire probably needed to bat for another 10 overs to make the game safe.

This was a pitch rated "Test quality" by Kent assistant coach Allan Donald. So, though Sean Dickson fell early, playing across one from Brookes, Zak Crawley and Matt Renshaw ensured there was to be no mistake. Crawley, who might well be the most outstanding top-order prospect in English cricket, dealt with the short ball with impressive ease and, throughout the match, used the sweep - both reverse and conventional - to nullify the threat from Patel. Renshaw negotiated a sticky start - he didn't play the short ball as well as Crawley - to see his side home.

Kent's first victory in Division One since September 2010 - and their first at Edgbaston in the Championship since 2005 - was achieved with nine-and-a-half overs remaining.

Given the fortunes of recently promoted clubs in recent times, this may prove an important result for both sides. Certainly it will provide confidence within the Kent dressing room. And while their attack still lacks a bit of pace, they should be boosted by the return of Sam Billings and Joe Denly before too long. Few expect them to finish in the top half of the table, but they proved here they may make a better fist of survival than some promoted sides.

This is a worrying reverse for Warwickshire. While they can claim some mitigation - they were without a number of first-choice players through injury - they will also know that some of their batting was flimsy and some of their bowling lacked control or consistency. They looked, in short, like a team struggling to come to terms with the higher standard in Division One. It is hard not to conclude that it is matters at the bottom and not the top of the table that will be the focus of their attentions towards the end of the season.

"We were outbatted, outbowled and outfielded," their head coach, Jim Troughton, admitted afterwards. "We have just been outbasic-ed really and that is something we are going to have to instil in this group of young players."

Perhaps it need not have been such a young team. The likes of Chris Wright, Rikki Clarke and Keith Barker continue to ply their trade elsewhere, while the sight of Jonathan Trott in a Kent tracksuit (it was his first day at the club in a new, short-term coaching role) underlined the sense that Warwickshire might have utilised the services of those they have let go just a bit longer. For a club this size to be signing a player - Tom Milnes - on a match-by-match basis doesn't scream of great planning. Or perhaps performances like this are part of a transitional phase and patience will have to be given to young players as they bed in. A glance at Surrey, however, would suggest the two don't have to be exclusive.

"I am very proud of the guys," Donald said of his Kent team. "It was a very clinical performance with the bat, with really good hundreds from Crawley and Ollie Robinson.

"Taking 20 wickets on this pitch was a fantastic effort. I don't think I have ever seen a pitch that good at Edgbaston. The groundsman said to me 'get ready for a long haul' and that is absolutely what we got but it was a really strong bowling performance. We have been relentless with the ball and thoroughly earned the win. It's been a tremendous performance."