This paper uses a correlational research design to investigate the predictive power of the sources of self-efficacy and non-routine problem-solving achievement. It collected the data from a sample of 118 high-achieving secondary school learners in the Gauteng province, South Africa, using questionnaires, a problem-solving test, and interviews. Their self-efficacy beliefs were categorized into mastery experience, vicarious experience, social persuasion, and physiological state. The findings revealed that the physiological state, vicarious experience, and mastery experience self-efficacy beliefs had a positive impact on problem-solving achievement, whilst that of social persuasion was negative. The magnitudes of the impact of the physiological state and social persuasion sources of self-efficacy were relatively greater than the others. Each source of self-efficacy was discovered to have an insignificant weak positive linear relationship with problem-solving achievement.