The Italian hit the front with 100 metres to go and powered past his sprint rivals to take his first-ever win at his home grand tour.
But, a big crash with just 3.6 kilometres to go was the big talking point with some big general classification leaders losing time on Remco Evenepoel (23), who managed to remain unscathed, as he kept his maglia rosa after finishing in the front group.
Milan said after the win: “It is incredible and I am really happy, I cannot believe it. It is my first Giro and the second stage, I was pushing good in the time trial, but I could never imagine a victory was coming today.”
Groves spoke of his third position on the stage: "It was a fantastic ride by the guys to keep me in the front and position well for the sprint.
"There are things to improve, we went a bit early maybe but I was there to do a sprint and I hit out, but maybe it was a little too far for me.
"Things are looking good for the rest of the Giro."
Milan took over the points jersey from Filippo Ganna (26) after winning the stage
After yesterday’s fireworks in the opening time-trial, the peloton was expected to have a somewhat serene day on the coastal roads of the Abruzzo region before a hectic finale.
The breakaway went from kilometre zero with the four riders of Stefano Gandin (27), Thomas Champion (23), Paul Lapeira (22) and Mattia Bais (26) all slipping off the front with zero resistance, eventually joined by Alessandro Verre (21) 10 kilometres later.
They got a gap of five minutes and 37 seconds after 12 kilometres before Trek-Segafredo took over the chase in service of their sprinter Mads Pedersen (27).
The gap slowly tumbled as the quintet went over the two category four climbs in the middle of the stage and the peloton continued their way through the 202km day of racing.
With the King of the Mountains jersey up for grabs from the break, it was Lapiera of AG2R La Mondiale who would take it off the shoulders of Tao Geoghegan Hart (28) after cresting both summits first from the small group out front.
Verre and Lapeira would drop back to the peloton later on, leaving the trio of Gandin, Champion and Bais to be swept up by the pack with 38 kilometres of racing left in the day.
Those would be fast and furious with Trek and Alpecin-Fenix setting the pace - as they had done all day - before Soudal Quick-Step and Jumbo Visma arrived at the front with around 20 kilometres to go to protect their GC leaders Evenepoel and Primoz Roglic (33).
The main pinch-point in the finale was a roundabout with 1.4 kilometres to go, which the riders would have to take the outside of, diving left into the seafront finish in the town of San Salvo.
But a crash at 3.7km then sent shockwaves through the bunch. On a narrow road, a touch of wheels in the bunch sent riders sprawling as a leading group of around 40 went clear. Given the crash happened outside the three-kilometre safe zone, GC times will have big implications for the race.
Due to the size of the group, the roundabout played little part in the run-in and Alpecin-Fenix were the team least affected by the crash - they piloted their sprinter, Groves, into pole position.
Fernando Gaviria (28) launched first with 250 metres to go and was soon followed by Pascal Ackermann (29), but it was the Italian Milan who finished fastest to take his first-ever Giro D’Italia stage victory, letting out a scream of joy as he crossed the line.
As riders came home in dribs and drabs, it was unclear who lost time, with the race organisers yet to update the general classification. However, Geohegan Hart lost 19 seconds to fall further behind the race leader Evenepoel.
"Everything was pretty fine. We were in front so we were out of trouble but it was a nasty crash," the Belgian said.
"I actually saw it happen. We know who we can blame for this crash, but that's racing, it's not a nice move but luckily we stayed out of trouble and arrived safe."
