But his Team Sky team-mate Chris Froome lost ground on race leader, Australian Richie Porte, and will start one minute and two seconds down on Sunday’s final stage.
Manxman Kennaugh, who is still hoping to make next month’s tour, shrugged off Ben Swift (Emirates) to go solo over the Alpe d’Huez.
Kennaugh told Team Sky’s website: “I didn’t even know I was coming to this race a week before.
“I was at altitude training in preparation for the Tour de Suisse and then three days before the race they said I had to come here because of injury and illness.”
Pressed on his Tour de France prospects, Kennaugh added: “I’m sure they’ll pick the best team.
“For me, if I go to the Tour then great, if I don’t, I’ve got another baby on the way in early August and I’ll re-set my goals for the Vuelta (a Espana).”
Kennaugh pulled away from Swift on the final climb up towards the finish and won the stage from his rival by 13 seconds.
But Froome was punished for some gruelling early work as Porte piled on the pressure in the closing stages, adding 25 seconds to his existing advantage over the three-time winner.
In England, Sarah Roy sprinted to victory in stage four of the OVO Energy Women’s Tour of Britain in Chesterfield. The Orica rider, pictured, pipped Luxembourg’s Christine Majerus (Boels Dolmans) to victory in the last 100 metres after the pair moved clear of the peloton midway through the 123km stage.
Poland’s Katarzyna Niewiadoma (WM3 Pro Cycling) finished safely in the main group and will take a lead of one minute and 25 seconds into today’s fourth and final stage in London. Conscious of the need to eat into the overall leader’s advantage, Majerus did most of the work in breaking away from the pack. But despite moving to second in the general classification and trimming Niewiadoma’s overall lead to six seconds, it is unlikely to be enough to overcome the Pole.
Scotland’s Katie Archibald (Team WNT) suffered a fall towards the end of the stage which scuppered her hopes of improving on her eighth place at the start of the stage.