Belgian Jasper Philipsen (24) was second and Italy's Alberto Dainese (24) came home third.
Laporte's Jumbo-Visma team mate, Jonas Vingegaard (25) of Denmark, retained the overall leader's yellow jersey.
Dane Vingegaard was on the wrong side of a late split but the race jury gave the chasing bunch the same time as Philipsen and Dainese, although they crossed the line five seconds off the pace.
Vingegaard still holds a comfortable lead of 3:26 going into Saturday's final time trial, a 40.7-km effort between Lacapelle-Marival and Rocamadour.
Laporte, a decent sprinter who had not had an opportunity for a stage victory this year, was given the green light by his sporting directors to go for it on Friday and he duly delivered, after French riders had gone 38 stages without a Tour win.
They had not won a stage since world champion Julian Alaphilippe, who is not in this year's race as he recovers from injury, prevailed on the opening day last year.
After Quinn Simmons, the last survivor of the first breakaway group, was reined in by the peloton with 34 kilometres to go, France's Alexis Gougeard jumped away from the pack.
Pogacar, in yet another attempt to catch Vingegaard off guard, attacked in the descent from the Cote de Daunes but he was brought back by Van Aert.
Gougeard was joined by Fred Wright and Jasper Stuyven and the trio opened a 30-second gap but the sprinters' teams had slashed it down to a handful of seconds with two kilometres to go.
Van Aert sacrificed his own chances to further reduce the deficit, allowing Laporte to make the jump to catch Wright and Stuyven.
He stayed on Stuyven's wheel for a short while before launching his sprint at the right moment, holding his head in disbelief as he crossed the line.