Mark Cavendish won his 28th Tour de France stage after a photo finish with Andre Greipel in Angers.
The win drew the 31-year-old Manxman level with Frenchman Bernard Hinault's tally - only 34-time stage winner Eddy Merckx of Belgium is ahead of him.
There was initial confusion at the end as Greipel celebrated before Cavendish was named winner of the 223.5km stage.
Defending champion Chris Froome finished safely in the peloton, while Peter Sagan retained the race lead.
Two-time winner Froome moves up to fourth overall, 14 seconds behind world champion Sagan.
He was delivered to the line by his Team Sky squad on a day devoid of stress for the favourites for overall victory.
Colombia's Nairo Quintana, twice a runner-up to Froome, double winner Alberto Contador and Italian hope Fabio Aru also all finished in the main bunch.
Cavendish back on top
"Who thought when I started cycling that I would have my name mentioned in line with Bernard Hinault and Eddy Merckx. It's pretty amazing," said Cavendish, who added that he thought he had won despite Greipel's celebration.
"I know when I win and lose a photo finish and I thought I had it but I still had to wait," he said.
"It was so hairy in the finish but we planned it and I knew I had to come from behind. I wanted to be behind Greipel. After I didn't win the first stage last year I was anxious, a bit like Andre today.
"My team-mates were phenomenal again. Bernie Eisel and Mark Renshaw did a fantastic job."
The Dimension Data rider, who is competing in his 10th Tour de France, picked up his first win on stage five in 2008.
Since then, he has steadily accumulated 27 more, including stage one of this year's race, to equal five-time Tour winner Hinault's tally.
Cavendish will never win the Tour de France because he will always lose time in the hillier stages, as happened on Sunday's second stage, but he will be remembered long after he is gone for his remarkable feats.
Sprint rivals Greipel and Marcel Kittel are the closest active riders to Cavendish; the Germans have won 10 and eight stages respectively.
Sagan stays in yellow
Tinkoff rider Sagan spent much of the day on the front of the peloton chatting to fellow riders, enjoying his first ever day in the race leader's yellow jersey.
When the pace increased in the final 40km or so, he followed the wheels of his team-mates before finishing fourth in the sprint for the line to ensure he retained the overall lead.
"Today was a very relaxing day for us because in the breakaway there was only one rider," the Slovak said.
"He went slow, we went slow also in the group, it was nice. I was thinking in one moment that we would take a coffee, we had time. I saw a bar but afterwards there was no time."
How did the race unfold?
The pace was largely pedestrian after French rider Armindo Fonseca made a solo break in the first metres of the race and the peloton allowed him to build up a lead of more than 11 minutes.
Tommy Voeckler, a veteran of 14 Tours de France, asked the permission of the peloton before setting off in pursuit of Fonseca, who rides for Fortuneo Vital Concept, with around 90km of the stage remaining.
The Direct-Energie rider, 37, quickly bridged what had become a five-minute gap but the break was never likely to succeed.
The duo were finally caught in the final 10km as the teams of the sprinters jostled for the best position on the run-in to Angers.
Tuesday's fourth stage is the longest of the race at 237.5km and takes the riders from Saumur to Limoges.
A sprint finish is again expected. There is a slight uphill kick to the finish line but should Cavendish be victorious he will move second on his own on the all-time list.
The BBC Sport website will have live text commentary from 12:00 BST with radio commentary from 15:00 BST.
Stage 3 result:
1. Mark Cavendish (GB/Dimension Data) 5hrs 59mins 54secs
2. Andre Greipel (Ger/Lotto) Same time
3. Bryan Coquard (Fra/Direct Energie)
4. Peter Sagan (Svk/Tinkoff)
5. Edward Theuns (Bel/Trek)
6. Sondre Enger (Nor/IAM Cycling)
7. Marcel Kittel (Ger/Etixx - Quick-Step)
8. Christophe Laporte (Fra/Cofidis)
9. Daniel McLay (GB/Fortuneo)
10. Dylan Groenewegen (Ned/LottoNL)
General classification after stage 3:
1. Peter Sagan (Svk/Tinkoff) 14hrs 34mins 36secs
2. Julian Alaphilippe (Fra/Etixx - Quick-Step) +8secs
3. Alejandro Valverde (Spa/Movistar) +10secs
4. Chris Froome (GB/Team Sky) Same time
5. Warren Barguil (Fra/Giant) +14secs
6. Nairo Quintana (Col/Movistar)
7. Roman Kreuziger (Cze/Tinkoff)
8. Tony Gallopin (Fra/Lotto)
9. Fabio Aru (Ita/Astana)
10. Daniel Martin (Ire/Etixx - Quick-Step)