The origin of initial rotation rates of stars, and how a star's surface rotational velocity changes during the evolution, either by internal angular momentum transport or due to interactions with a binary companion, remain open questions in stellar astrophysics. Here, we aim to derive the physical parameters and study the distribution of (projected) rotational velocities of B-type stars in the 35 Myr-old, massive cluster NGC 330 in the Small Magellanic Cloud. NGC 330 is in an age range where the number of post-interaction binaries is predicted to be high near the cluster turnoff (TO). We develop a simultaneous photometric and spectroscopic grid-fitting method adjusting atmosphere models on multi-band Hubble Space Telescope photometry and Multi Unit Spectroscopic Explorer spectroscopy. This allows us to homogeneously constrain the physical parameters of over 250 B and Be stars, brighter than mF814W=18.8mag. The rotational velocities of Be stars in NGC 330 are significantly higher than the ones of B stars. The rotational velocities vary as a function of the star's position in the color-magnitude diagram, qualitatively following predictions of binary population synthesis. A comparison to younger clusters shows that stars in NGC 330 rotate more rapidly on average. The rotational velocities of the 35Myr old population in NGC 330 quantitatively agree with predictions for a stellar population that underwent significant binary interactions: the bulk of the B stars could be single stars or primaries in pre-interaction binaries. The rapidly spinning Be stars could be mass and angular momentum gainers in previous interactions, while those Be stars close to the TO may be spun-up single stars. The slowly rotating, apparently single stars above the TO could be merger products. The different vsini-characteristics of NGC 330 compared to younger populations can be understood in this framework.