Background: Previous research suggests that many individuals with autism spectrum disorder (ASD) have impaired facial identity recognition, and also exhibit abnormal visual scanning of faces. Here, two hypotheses accounting for an association between these observations were tested: i) better facial identity recognition is associated with increased gaze time on the Eye region; ii) better facial identity recognition is associated with increased eye-movements around the face. Methodology and Principal Findings: Eye-movements of 11 children with ASD and 11 age-matched typically developing (TD) controls were recorded whilst they viewed a series of faces, and then completed a two alternative forced-choice recognition memory test for the faces. Scores on the memory task were standardized according to age. In both groups, there was no evidence of an association between the proportion of time spent looking at the Eye region of faces and age-standardized recognition performance, thus the first hypothesis was rejected. However, the 'Dynamic Scanning Index' - which was incremented each time the participant saccaded into and out of one of the core-feature interest areas - was strongly associated with age-standardized face recognition scores in both groups, even after controlling for various other potential predictors of performance. Conclusions and Significance: In support of the second hypothesis, results suggested that increased saccading between core-features was associated with more accurate face recognition ability, both in typical development and ASD. Causal directions of this relationship remain undetermined.