ABSTRACT Known for their efficiency in analysing large data sets, machine learning-based classifiers have been widely used in wide-field sky survey pipelines. The upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will generate millions of real-time alerts every night, enabling the discovery of large samples of rare events. Identifying such objects soon after explosion will be essential to study their evolution. Using ∼5400 transients from the Zwicky Transient Facility (ZTF) Bright Transient Survey as training and test data, we develop NEEDLE (NEural Engine for Discovering Luminous Events), a novel hybrid (convolutional neural network + dense neural network) classifier to select for two rare classes with strong environmental preferences: superluminous supernovae (SLSNe) preferring dwarf galaxies, and tidal disruption events (TDEs) occurring in the centres of nucleated galaxies. The input data includes (i) cutouts of the detection and reference images, (ii) photometric information contained directly in the alert packets, and (iii) host galaxy magnitudes from Pan-STARRS (Panoramic Survey Telescope and Rapid Response System). Despite having only a few tens of examples of the rare classes, our average (best) completeness on an unseen test set reaches 73 per cent (86 per cent) for SLSNe and 80 per cent (87 per cent) for TDEs. While very encouraging for completeness, this may still result in relatively low purity for the rare transients, given the large class imbalance in real surveys. However, the goal of NEEDLE is to find good candidates for spectroscopic classification, rather than to select pure photometric samples. Our system will be deployed as an annotator on the UK alert broker, Lasair, to provide predictions of real-time alerts from ZTF and LSST to the community.