AG2R La Mondiale rider Geniez held firm as an early 18-rider breakaway was whittled down to sprint home ahead of Team Sky’s Dylan van Baarle and Mark Padun of Bahrain-Merida.
Spain’s Jesus Herrada did enough to grab the lead in the overall classification with an advantage of three minutes and 22 seconds over the now second-placed Yates.
Herrada had been part of the initial breakaway but fell away to finish just over two minutes behind the leading pack, with the peloton which included Yates almost 12 minutes back.
Geniez’s win was marred when he swerved to avoid photographers and crashed into a race official shortly after crossing the finish line, bringing down a number of other riders including Van Baarle.
The 181km stage saw a series of attacks from the start until a prominent bunch including the likes of Geniez, Van Baarle and Vincenzo Nibali managed to establish an advantage of over 10 minutes.
A further attack split the leading group but Geniez and Dylan Teuns (BMC) were among those to haul them in, while Herrada hung in in his bid to claim the red jersey.
Despite sporadically losing touch with the leaders, Geniez and Van Baarle worked themselves back into contention and set up the final sprint in which the Frenchman stole a march on his rivals.
Herrada will take his advantage into the forthcoming stages in the Asturias and Leon mountains, while Spanish veteran Alejandro Valverde (Movistar) remains one second behind Yates in third place.
UAE Team Emirates’ Diego Ulissi returns to the stage of his last one-day race win as the Italian gears up for the Grand Prix Cycliste de Quebec and the Grand Prix Cycliste de Montreal later this week.
The 29-year-old took home first place in the GP Montreal last year, his second one-day victory in UAE colours, and will be hoping for a repeat performance this time round.
Joining Ulissi will be former European Champion Alexander Kristoff, alongside teammates Rui Costa, Alexandr Riabushenko, Manuele Mori, Marco Marcato and Jan Polanc.
Commenting ahead of the race, the Lugano resident said: “The GP Québec and the GP Montréal are two races that I particularly like. They are classics that are similar to the world championships.
“Among the two, I like Montréal because it’s a little harder than Québec and it’s more open to attackers. I had a fever a few days ago so I am not heading into the races in the best shape , but let’s see how my body will respond under force. I hope I can defend the title I won last year in Montréal.”
Italian Alessandro Tonelli claimed the overall lead in the Tour of Britain despite losing a sprint finish to Australian Cameron Mayer on the second stage.
Tonelli, of the Bardiani-CSF team, took a six-second time bonus on the line which meant he claimed the green jersey on the 108-mile Cranbrook to Barnstaple stage in Devon.
Meyer, the Commonwealth Games time trial champion, edged out the Italian on the finish line after a day-long breakaway.
The Michelton-Scott rider, who last claimed a road race victory in February 2015, and Tonelli had been a part of the main group which went clear in the opening nine miles.
“I’ve been here at the Tour of Britain six or seven years ago when I was caught in the last kilometre so I was hoping there was no deja vu,” Meyer told ITV 4.
“I just picked my moment to go across to four guys and we had a breakaway of five. In the end it was a great bike race for me and a thrilling finish.
“It was a bit of a shock to take the win. We’ll see what I can do for the rest of the tour.”
New Zealander Patrick Bevan currently sits third in the overall classification, just eight seconds behind with Team Sky’s Dutchman Wout Poels leading the chasing group.
British duo Scott Davies, having taken the King of the Mountains jersey, and Hugh Carthy are both within 22 seconds of the leader.
“It was a hard stage. A group of five went early on and I just tried to sweep up the KoM points,” said Team Dimension Data’s Davies.