Andrejs Trofimovics, 25, was found stabbed at a flat in Cleveland Road, in the Springbourne area of the town.
Vladislav Pomozov, 45, of Holdenhurst Road, Bournemouth, was found guilty of murder and of wounding with intent.
He was remanded in custody and is due at Winchester Crown Court for sentencing on 6 July.
Mr Trofimovics, from Riga in Latvia, died from a single stab wound, a post-mortem test concluded.
Dorset Police said Latvian national Pomozov was the partner of Mr Trofimovics' mother.
The stabbing followed a "minor confrontation" between Mr Trofimovics and Pomozov at a New Year's party, which was held at Mr Trofimovics' father's flat, police added.
Pomozov was found not guilty of the attempted murder of Mr Trofimovics' father Jevgenijs who sustained non-life threatening injuries.
Following the conviction, Det Sgt Mark Jenkins described Mr Trofimovics' death as "tragic and avoidable".
A man has been found guilty of murder after a man was stabbed to death at a flat in Bournemouth on New Year's Day.