The Danish champion was part of a move that bridged across to a leading group of five riders in the last 7 kilometres before having to chase down another attack by Kasia Niewiadoma (Canyon-SRAM) and Elisa Longo Borghini (Trek-Segafredo) inside the final 3 kilometres.
Ludwig waited to begin her sprint on the uphill drag to the finish, coming around Niewiadoma before comfortably beating yellow jersey Marianne Vos (Jumbo-Visma) with time to extend her arms in celebration of an emotional stage victory.
Vos finished second and remained in the overall lead while Ashleigh Moolman-Pasio (SD-Worx) came in third.
"It feels like such a good comeback after a really bad day yesterday, losing Marta (Cavalli), crashing and having to come back," a jubilant Ludwig said following the stage.
"But I just loved how the team kept the fighting spirit. We knew today was a super good day and if I had the legs then I could try and go for the win.
"To actually do it and be a Tour de France stage winner, in this jersey... Oh my god, it doesn't get better."
There were multiple attacks in the early stages of the race from Reims to Epernay, but more flat exposed roads in windy conditions made it difficult for any breakaway hopefuls to carve out a significant gap on the peloton.
All riders were back together as they hit the base of the Cote de Vertus and Femke Gerritse (Parkhotel Valkenburg) consolidated her lead in the Queen of the Mountains classification, beating out Elise Chabbey (Canyon SRAM) for the two points on offer before taking two more on the Mesnil-sur-Oger 8 kilometres later.
Alena Amialiusik (Canyon-SRAM) then embarked on a solo move with 44 kilometres to go, gapping the peloton by as much as a minute through the forest section of the parcours.
Then there were crashes with 17 kilometres left, Australian Rachel Neylan (Cofidis) going down through a corner but appearing relatively unharmed and continuing her race.
Amialiusik was reeled in up ahead by a group of the race favourites, Demi Vollering (SD Worx) taking control of that group until she too crashed around a corner along with Liane Lippert (Team DSM), leaving Annemiek van Vleuten (Movistar), Moolman-Pasio, Silvia Persico (Valcar–Travel & Service), Margarita Victor García (UAE Team ADQ) and Elisa Longo Borghini (Trek-Segafredo) to go up the road.
It then became two strong groups in battle with each other, the hunters of Vollering, Ludwig, Vos, Juliette Labous (Team DSM), Niewiadoma and Alexandra Manly (BikeExchange-Jayco) hunting Longo Borghini, Van Veuten, Margarita Victoria García (UAE Team Emirates), Silvia Persico and Moolman-Pasio.
Bridging successful, Moolman-Pasio counterattacked an earlier move to split the group again as van Vleuten was dropped completely, her stage hopes done with four kilometres left.
Moolman-Pasio, Longo Borghini and Vollering were caught just before the 2 kilometre to go banner, the group contesting the finish with Niewiadoma leading out the sprint from 300 metres out, side-by-side with Vos until Ludwig shot across the road around both of them to win the stage with a powerful kick to the line.
The Tour de France Femmes continues tomorrow night with a hilly 126.8 kilometre stage from Troyes to Bar-Sur-Aube. Watch the action from the early time of 10:15pm (AEST) on the SBS SKODA Tour Tracker before SBS and SBS On Demand coverage begins from 10:30pm (AEST).
