The first half saw the lead exchanged several times as Cardiff opened the scoring with an early try from Josh Adams, who also dotted down for a brace.
With four tries for Cardiff and six for Bath, there was scoring aplenty, with scores also coming from Joe Cokanasiga, Ollie Lawrence, Alfie Barbeary and Dunn.
Finn Russell slotted nine points and earned himself the player of the match medal, using his boot-to-ball skills to open up the backs.
Cardiff Rugby 32
Tries: Josh Adams (2), Gabriel Hamer-Webb, Ben Thomas.
Conversions: Tinus de Beer (3).
Penalties: Tinus de Beer (2).
Bath Rugby 39
Tries: Joe Cokanasiga, Ollie Lawrence, Alfie Barbeary, Tom Dunn, Jaco Coetzee (2).
Conversions: Finn Russell (3).
Penalties: Finn Russell.
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