THey have liquid bottles of Dental Care Liquid It is a blueish liquid and you put a couple drops into the dogs water bowl. That easy and it does take a few days to notice but keep it up it will help, some.
You didn't mention the age of your dog, but the answer is most likely gum disease - possibly even an abscess. Once it gets to the stage you are describing, a vet check and thorough professional cleaning is usually necessary. Then you follow up with the weekly brushing and things like greenies. It sounds expensive, but left unattended, the outcome is loss of teeth or even systemic infection. Don't just try to cover it up. The source of the problem won't go away.
I agree it is more than likely periodontal disease. Most kibble fed dogs/cats have it by age 2.
I raw feed, which solves the bad breath problem, along with a lot of other problems kibble fed dogs have, but if you don't want to actually go to raw feeding, a nice big meaty beef bone several times a week does wonders. Also raw chicken with bone cleans the teeth beautifully and gives them sweet smelling breath.