。
She was taken in by the salesman's smooth talk.
Literal
She [topic-は] salesman [genitive-の] mouth-tip [genitive-の] skillfulness [by-に] was-deceived.
口先 (literally 'tip of the mouth') refers to surface-level talk — words without conviction or follow-through behind them. 口先のうまさ is then 'skill at superficial talk', with うまさ being the noun form of うまい ('skillful / good at') via the productive ~さ suffix that turns adjectives into abstract nouns. The whole noun phrase is the agent of the passive verb だまされる, with passive agents marked by に. Note Japanese passives are often used to express a speaker's negative experience — being taken advantage of, made to suffer — making them feel more emotionally weighted than English passives.