It was a tense final in Carcassonne as riders fought for position to get into the final kilometres in perfect position, but Cavendish showed his class to outsprint Jasper Philipsen (Alpecin-Fenix) and Iván García (Bahrain-Victorious).
The Manxman now has 34 stage wins in the Tour de France, equalling the record set by Eddy Merckx.
Cavendish's Deceuninck - Quick-Step lead-out rider Michael Mørkøv also sprinted to a phenomenal second place.
Tadej Pogačar (UAE Team Emirates) finished safely in the bunch to maintain his race lead for another day.
How it happened
Stage 13 of the 2021 Tour de France looked to be another tense battle between the breakaway and the sprinters, after the breakaway secured the victory on stage 12.
Running over 219km from Nîmes to Carcassonne the undulating course featured one categorised climb, the Côte du Pic Saint-Loup (5.5km at 3.7 per cent), but with countless uncategorised climbs along the way.
The stage opened with another lively battle for a breakaway to form, with a number of groups looking like they had made the escape, before Deceuninck - Quick-Step would inevitably close down the gap.
After 30km, three riders finally got a gap however and were allowed enough of a leash to think about staying out for the day.
Omer Goldstein (Israel Start-Up Nation), Sean Bennett (Qhubeka-NextHash) and Pierre Latour (TotalEnergies) were the three riders to get away, as the peloton were happy to let them slip free.
The trio extended their advantage as they climbed the only categorised climb of the day, pulling out almost five minutes before the bunch decided to bring them safely back within range, mostly entirely under the impetus of Deceuninck - Quick-Step’s Tim Declerq.
As the breakaway then swept up the points at the intermediate sprint, 113km from home, Sonny Colbrelli (Bahrain Victorious) led the bunch across the line to take 13 points in the green jersey competition, followed by Michael Matthews (Team BikeExchange).
Cavendish didn’t challenge the sprint, but still secured eight points.
The race was then calm until around 70km from the line, when Philippe Gilbert (Lotto-Soudal) lit things up in the bunch with a surprise attack, sparking another flurry of attacks in the bunch.
That caused a reaction from the breakaway, with Goldstein sprinting away from his companions with only Latour able to follow, as Bennett was quickly dropped.
But the accelerations also caused a crash in the bunch around 62km out, with Simon Yates (Team BikeExchange) and Tim Declerq among the large group of riders that fell into a steep ravine after the incident on a gradual left-hand turn.
Yates tried to rejoin the peloton, but eventually abandoned the 2021 Tour de France.
The breakaway was finally caught 53km from the line, with Quentin Pacher (B&B Hotels p/b KTM) launching a solo attack and quickly pulling out a minute gap as the bunch slowed.
Pacher was caught 20km from home, as the GC teams moved up to race for the extended 4.5km cut-off point for overall times.
Into the final 4.5km and Deceuninck swept to the front of the bunch to take over from Ineos Grenadiers, with Kasper Asgreen leading into the final 2km before Bahrain Victorious also tried to move up.
Into the final kilometre and Deceuninck led once again with a full strength lead-out, but Team DSM surged up suddenly bringing up a handful of other riders,with Cavendish looking blocked in with 500m to go.
Cavendish found himself behind Nacer Bouhanni (Arkéa-Samsic), but he found his way back to Michael Mørkøv’s wheel inside the final 250m.
Ivan Garcia (Movistar) launched an early sprint and looked like he might sneak the victory, but Mørkøv pulled hard to get Cavendish back into the fight, with Cavendish launching his sprint inside the final 25m, blasting past Philipsen, Garcia and Mørkøv to make history.
The Tour de France 2021 continues with a brutal mountain stage in the Pyrenees on stage 14, from Carcassonne to Quillan, over 183km.
Tour de France 2021, stage 13: Nîmes to Carcassonne (219.9km)
1. Mark Cavendish (GBr) Deceuninck-Quick-Step, in 5-04-29
2. Michel Mørkøv (Den) Deceuninck-Quick-Step
3. Jasper Philipsen (Bel) Alpecin-Fenix
4. Iván García Cortina (Esp) Movistar Team
5. Danny van Poppel (Ned) Intermarché - Wanty - Gobert Matériaux
6. Alex Aranburu (Esp) Astana-Premier Tech
7. Christophe Laporte (Fra) Cofidis
8. André Greipel (Ger) Israel Start-Up Nation
9. Magnus Cort (Den) EF Education-Nippo
10. Jasper Stuyven (Bel) Trek-Segafredo, all at same time
General classification after stage 13
1. Tadej Pogačar (Slo) UAE Team Emirates, in 52-27-12
2. Rigoberto Urán (Col) EF Education-Nippo, at 5-18
3. Jonas Vingegaard (Den) Jumbo-Visma, at 5-32
4. Richard Carapaz (Ecu) Ineos Grenadiers, at 5-33
5. Ben O'Connor (Aus) Ag2r-Citroën, at 5-58
6. Wilco Kelderman (Ned) Bora-Hansgrohe, at 6-16
7. Alexey Lutsenko (Kaz) Astana-Premier Tech, at 6-30
8. Enric Mas (Esp) Movistar Team, at 7-11
9. Guillaume Martin (Fra) Cofidis, at 9-29
10. Pello Bilbao (Esp) Bahrain-Victorious, at 10-28
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