Cecilie Uttrup Ludwig (Cervelo-Bigla Pro) and Grace Elvin (Orica-Scott) led a breakaway group of five, which also included Amy Pieters, the Dutch Boels-Dolmans rider who had claimed victory on stage two in Stoke-on-Trent, and Martina Ritter (Drops), but were eventually chased down with five kilometres left.
There was, though, a crash as the peleton closed in, which saw Pieters caught up along with Marianne Vos (WM3), who had been in second place overall, and Dani King (Cylance Pro).
Hosking, however, got her positioning right heading into the last 100 metres of the narrow rising finish on the Parade, where she edged ahead of Barnes and Ellen van Dijk (Team Sunweb), with Giorgia Bronzini (Wiggle High5) in fourth place.
The 26-year-old from Victoria said: "This is a highlight race for most riders on the calendar, so I feel really privileged to come away with my first win and first podium here. It is a phenomenal event, I feel like I have entered an elite group.
"There was a group of five that got away and for me that was a bit worrying. It took a bit of effort to drag them in. Once we caught them everybody switched their mindset to a bunch sprint.
"It was a bit chaotic, which is strange because it was probably the least technical finish we have all week, but it was nice that the sprinters got a chance."
Niewiadoma, meanwhile, managed to stay clear of any trouble as the WM3 rider kept the overall lead in the green jersey general classifications, although her advantage dropped to one minute and 31 seconds as Van Dijk moved up to second.
Alice Barnes is in joint third alongside her sister Hannah (Canyon-SRAM) and Vos, who was unable to contest the finish after crashing within the final 500m, on the same time, all 1min and 46secs off the pace.
"This year has been a breakthrough season, I have trained really hard and I am happy it is paying off," Alice Barnes said.
"The Women's Tour is a home race for me, a Women's WorldTour event and it is one of the biggest on the calendar, so well organised and everybody comes here wanting to win it, so you have to go into it with good focus and train hard for it."
Hannah Barnes had finished Wednesday's stage in second place, and Alice, 21, is relishing the chance to race alongside her older sister.
"There is not really any sibling rivalry between us. Everybody thinks there should be, but we just race the events and try and get the best results we can," she said at the post-stage press conference.
"We are actually closer now I am racing on the road than when I was a mountain biker."
Friday's fourth stage runs over 123.1 kilometres around Chesterfield, which includes the most climbing with over 2000m of ascent.
