Alpecin-Deceuninck's Groves, 26, pipped Belgian Milan Fretin and Frenchman Paul Magnier at the line after winning a stage on the Giro in 2023.
Lidl-Trek's Pedersen finished comfortably more than five minutes behind after a ride of 227km, having re-taken the lead on stage three.
The race was neutralised with around 70km to go after a mass crash forced Groves' compatriot Jai Hindley to withdraw, three years on from winning the race.
After the incident, the riders continued to move forward at a slower pace for around 20km before a new start was given and racing resumed towards the finish.
The organisers then announced all the riders would be classified in the same time and no bonuses would be awarded at the finish, with only the stage victory on the line.
With 10km to go, the peloton arrived on the outskirts of the southern city, with conditions dry after downpours earlier in the day.
Frenchman Enzo Paleni and Dutchman Taco van der Hoorn then attempted to break away but were caught with 2.5km left.
In the final kilometre, alongside the port, Wout van Aert made a preemptive split before Groves powered past him for victory.
Following the earlier incident, Hindley climbed into an ambulance after sitting on the pavement for several minutes following a crash that occurred around 150km from the start in Potenza, inland to the south of Naples.
On roads made very slippery by rain, many riders fell, including Ecuadorian Richard Carapaz, winner of the 2019 Giro, Frenchman Paul Magnier and Briton Adam Yates.
Hindley was the hardest hit and, despite being able to get up on his own, was forced to abandon, depriving Red Bull Bora teammate Primoz Roglic of an important ally in the mountains.
German rider Juri Hollmann was also forced to pull out with a suspected fractured arm, according to his team, Alpecin.
Friday's seventh stage is a mountainous 168km ride from Castel di Sangro to Tagliacozzo, just to the west of Rome, which includes three testing climbs.