We enrich the extended theory of planned behaviour (ETPB), to which we introduced two additional components – academic and computer literacy – to examine how different behavioural, moral and educational traits influence students’ intentions to plagiarise. We argue that the relationship between components of the ETPB and students’ intention to plagiarise is likely to be nuanced – and may display significant divergence depending on the students’ awareness of text matching software utilisation. Using a sample of around 400 students from the University of Montenegro, our results partly confirmed that the extended theory of planned behaviour is an accurate predictor of the students’ intention to plagiarise. More precisely, favourable attitudes towards plagiarism, low perceived behavioural control and low moral obligation influence positively students’ intention to plagiarise. On the contrary, low subjective norms as well as both low academic and high computer literacy are found to be not significantly related to the students’ intention to plagiarise. Further analysis reveals that the introduction of the moderator variable (students’ awareness of text matching software utilisation) weakens the relation between the ETPB’s components and students’ intention to plagiarise. Overall, the obtained findings undoubtedly demonstrate that students’ awareness of the utilisation of the text matching software acts as a strong impediment to the intention to plagiarise, mainly neutralizing the positive relations between the ETPB’s components and intention to plagiarise.