This study describes an intervention that introduced a period of solving non-routine problems into tertiary STEM lectures. The aim was twofold: to attempt to increase student engagement and to introduce them to the kind of domain-free abstract reasoning that involves critical, creative and innovative thinking. The study involved over 600 STEM participants in five lecture classes from three tertiary institutions. The results show that a style of lecture delivery that utilises the inherent engagement effect of non-routine problems can have a positive influence on student engagement -- the effect that extends to a group of students who are conformed to type on many measures, including low-achievement. This is supported by evidence from different sources, including data from naturalistic observations conducted in lectures before, during, and after the intervention delivery; cross-sectional survey data at the start and the end of the semester; and interview data from the participant lecturers. The intervention is amenable to scaling up with a relatively small development investment and easily transferable to other tertiary STEM courses.