Even with a massive mountain stage and a long individual time-trial to come later in the week, 24-year-old Eulalio and his Bahrain-Victorious have every chance of holding the overall lead and the pink jersey until the final stages.
Race favourite Jonas Vingegaard finished the stage seven minutes and 14 seconds down on the pair in treacherous conditions despite the duo falling due to the rain and Arrieta even taking a wrong turn in an event-filled day in the Giro.
Eulalio leads overnight leader Giulio Ciccone by six minutes and 14 seconds, with Egan Bernal and Vingegaard another handful of seconds further back.
As the peloton embarked from the pretty Calabrian seaside town of Praia a Mare, few expected such a relentless deluge in the rolling green hills to Potenza.
As the pair approached the finish, Arietta was first to fall at a corner with Eulalio then tumbling a few kilometres later.
But when Arietta took a late wrong turn it looked over for him, however, when he wept at the finish line, it was tears of joy and relief after he overtook his escape partner with metres to go.
The stage win is a surprise given that Team UAE lost Adam Yates, Jay Vine and Marc Soler in a pile-up on stage two.
"I was completely empty in the last kilometres, but I knew Eulalio was also the same, and both of us deserved the victory, but in the end I had it," said the Spaniard Arrieta, now second in the overall standings.
Another accident during the race concerned Tudor's Mathys Rondel, who miraculously emerged relatively unscathed after breaking the back windscreen of a UAE team car that had hit the brakes too suddenly.
Thursday's stage six should enjoy better weather as the race takes the peloton to the southern port city of Naples.