Slovakia's Sagan edged out Spain's Daniel Moreno and Thibaut Pinot of France in the finish at Olivone.
Dutchman Dumoulin finished with the leaders to maintain his five-second advantage over Moreno and Saga in second and third.
Britain's Geraint Thomas and Pinot, who was third at last year's Tour de France, round out the top five, separated by just 12 seconds.
Bad weather on the St-Gothard mountain saw the start of the stage moved from Brunnen to Quinto and the distance cut by more than 50km.
A three-man breakaway of Stefan Denifl, Marco Marcato and Branislau Samoilau built up a lead of six minutes on the peloton at one point but Sagan's Tinkoff team and Dumoulin's Giant outfit led the chase.
Once the trio were reeled in, a number of other riders tried to attack alone but Tinkoff chasaed hard to ensure Sagan reigned in the sprint.
Tuesday's fourth stage is over 193.2 kilometres from Flims Laax Falera to Schwarzenbach and is suited to a sprint finish.
CYCLING
Dumoulin holds on to Tour de Suisse lead
Peter Sagan sprinted to victory on the shortened 117.3-kilometre third stage of the Tour de Suisse cycling race on Monday as Tom Dumoulin maintained his overall lead.
CYCLING
Swiss rider dies after fall into ravine on Tour of Switzerland
Swiss rider Gino Maeder has died from the injuries he sustained when he plunged into a ravine during a stage of the Tour of Switzerland, his team Bahrain-Victorious said on Friday.
Maeder, 26, fell during a high-speed descent on the fifth stage between Fiesch and La Punt on Thursday, after an exhausting day marked by three ascents over 2,000 metres altitude.
He had been found “lifeless in the water” of a ravine below the road, “immediately resuscitated then transported to the hospital in Chur by air”, organisers said.
But the next day, “Gino lost his battle to recover from the serious injuries he sustained,” Bahrain-Victorious said in a statement.
“It is with deep sadness and heavy hearts that we must announce the passing of Gino Mäder,” his team wrote in a statement.
“On Friday June 16th, following a very serious fall during the fifth stage of the Tour de Suisse, Gino lost his fight to recover from the serious injuries he had suffered. Our entire team is devastated by this tragic accident, and our thoughts and prayers are with Gino’s family and loved ones at this incredibly difficult time.”
“Despite the best efforts of the phenomenal staff at Chur hospital, Gino couldn’t make it through this, his final and biggest challenge, and at 11:30am we said goodbye to one of the shining lights of our team,” the team said in a statement.
🙏🏻 Gino, thank you for the light, the joy, and the laughs you brought us all, we will miss you as a rider and as a person.
❤️ Today and every day, we ride for you, Gino.
🔗 https://t.co/CSx5BsWfRz pic.twitter.com/caBmfmWwyg
— Team Bahrain Victorious (@BHRVictorious) June 16, 2023
Maeder had enjoyed a strong start to the season, finishing fifth in the Paris-Nice race.
American rider Magnus Sheffield also fell on the same descent from Albula, during the most difficult stage of the race with multiple climbs. The Ineos-Grenadiers rider was hospitalised with “bruises and concussion,” organisers said.
On Thursday, world champion Remco Evenepoel criticised the decision to compete on such a dangerous road.
“While a summit finish would have been perfectly possible, it wasn’t a good decision to let us finish down this dangerous descent,” the Belgian wrote on Twitter.
“As riders, we should also think about the risks we take going down a mountain.”
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