Boasson Hagen launched a solo attack with three kilometres remaining and managed to stay out in front despite the efforts of the sprinters to chase him down.
Boom (Team LottoNL-Jumbo), also champion in 2011, began the stage in Worcester with a slender eight-second lead over Stefan Kung (BMC Racing Team) but did a good job protecting it as those still in with a chance of overall victory piled on the pressure.
"It's a great feeling," Boom said. "I didn't expect today to be that hard but with the intermediate sprints and then some really tough climbs in the beginning, it was really hard.
"The first hour was quite critical, we lost two guys from the team in the second peloton, but luckily some other guys came back so we were still quite strong. If we had to do something we could do something but the first hour was almost killing me!"
Boasson Hagen (Team Dimension Data) moved up to second overall ahead of Kung thanks to a 10-second bonus for winning the 180km eighth stage in the Welsh capital.
"It feels good to finally get this victory. We had a plan from the beginning of the day for me to try to attack with two or three kilometres to go," Boasson Hagen said.
His team mate Mark Cavendish, in his first race since being forced to pull out of the Tour de France injured following a crash, abandoned on the final day.