Barnes finished second on the 62km street race to move on to the podium as Belgium's Jolien D'Hoore won the stage, with Christine Majerus in third.
Luxembourg's Majerus finished second overall, 1:18 minutes behind Niewiadoma
Barnes' sister Alice was sixth with fellow Briton Dani King in ninth.
Britain's defending champion Lizzie Deignan finished 42nd overall, while Olympic team pursuit champion Katie Archibald was 18th.
1. Jolien D'Hoore (Bel/Wiggle High5) 1hr 28mins 23secs
2. Hannah Barnes (GB/Canyon SRAM Racing) same time
3. Christine Majerus (Lux/Boels Dolmans) same time
4. Roxane Fournier (Fra/FDJ) same time
5. Katie Archibald (GB/WNT) same time
1. Katarzyna Niewiadoma (Pol/WM3 Pro Cycling) 16hrs 34mins 53secs
2. Christine Majerus (Lux/Boels Dolmans) +1min 18secs
3. Hannah Barnes (GB/Canyon SRAM Racing) +1min 30sec

The 8-11 shot defeated 12-1 chance Algometer by one and a half lengths with the other four rivals well beaten.
Midterm is a son of 2001 Derby winner Galileo and Group One victor Midday.
After the Sandown win, Midterm's odds for the Derby at Epsom in June were cut by some bookmakers from 8-1 to 6-1 second favourite.
The 4-1 market leader is US Army Ranger.
In the 1980s, the trial was won by subsequent Derby winners Shergar and Shahrastani, although the last runner to triumph at Epsom was 1997 Sandown runner-up Benny The Dip.
You can check out the latest racing results on the BBC Sport website.
Britain's Hannah Barnes finished third on the Women's Tour as Poland's Katarzyna Niewiadoma claimed the overall title after Sunday's final stage in London.
[NEXT_CONCEPT]
Odds-on favourite Midterm, ridden by Ryan Moore for trainer Sir Michael Stoute, won the Classic Trial at Sandown on Friday afternoon.