Michael Matthews powered his way up the steep climb to the airfield in Mende to win his first Tour de France stage in five years and surely the finest of his four to date.

The 31-year-old made his name winning bunch sprints, but this time he attacked from a breakaway and then showed his maturity on the three-kilometre climb, named after 1995 winner Laurent Jalabert, at the end of this 192km stage from Saint Etienne.

Matthews kept his cool in temperatures touching 40 degrees centigrade as Alberto Bettiol passed him and briefly rode clear but then faded before the summit, allowing the Australian to come back around and enjoy his celebrations on the runway to the line.

Defending champion Tadej Pogacar tried to use the same climb, with gradients consistently in double digits, to distance Jonas Vingegaard as the main contenders came home more than 12 minutes later, but the yellow jersey immediately latched on to his wheel and stuck there to the line.

Geraint Thomas and Adam Yates could not follow, losing 17 and 22 seconds respectively, though they remain third and fifth overall.

The day, however, belonged to Matthews, a rider who won two stages and the points classification in the 2017 Tour but who has endured much frustration since – not least with second places behind Pogacar and Wout Van Aert on stages six and eight last week.

Matthews got himself in a 23-strong breakaway handed a comfortable advantage by the peloton, but was surrounded by better climbers.

He needed to take the initiative and did with an attack 52km from home which only Felix Grossschartner, Andreas Kron and Luis Leon Sanchez could follow.

After Kron suffered a puncture to continue Lotto-Soudal’s miserable run of luck, Matthews rode the other two off his wheel early on the final climb, where temperatures were such that a police car had overheated and gone up in flames hours before the riders arrived.

Bettiol emerged from a chase group who were 20 seconds behind when the road ramped up and the Italian powered his way past Matthews on the steepest section, 15 per cent, mid-way up, but the EF Education-EasyPost rider had invested too much, Matthews steadily reeling him in, then leaving him behind.

“In my career I’ve had so many rollercoasters up and down but my wife and my daughter, they kept believing in me,” said Matthews, who has surely helped himself in ongoing negotiations with BikeExchange-Jayco over a new contract.

“How many times have I been smashed down and all the time I get back up.

“This was for my daughter today. She’s four years old and I really just wanted to show her why I’m away all the time, to show her what it’s for. Today was that day.

“I wanted to show everybody I’m not just a sprinter. I can ride like I rode today.”

Having surrendered yellow on the Col du Granon, Pogacar has spent every day since trying to prove Wednesday’s entirely uncharacteristic collapse was a one-off.

The 23-year-old lit up the early part of this stage, following an attack from Van Aert which effectively split the peloton and distanced a number of Vingegaard’s team-mates – something that would prove significant as the yellow jersey was left isolated by the end.

Pogacar spied his chance and turned on the power around a third of the way up the incline, but Vingegaard had seen it coming and immediately followed, not leaving the Slovenian’s wheel until they crossed the line.

It was no surprise to see Thomas unable to match those moves on these gradients, but the Welshman stuck to his pace and limited his losses to 17 seconds, leaving him 21 behind Pogacar and two minutes 43 seconds off yellow.