Cognitive functions such as numerical processing and spatial attention show varying degrees of lateralization. Transcranial direct current stimulation (tDCS) can be used to investigate how modulating cortical excitability affects performance of these tasks. This study investigated the effect of bi-parietal tDCS on numerical processing, spatial and sustained attention. It was hypothesized that tDCS would have distinct effects on these tasks because of varying lateralization (numerical processing left, spatial attention right) and that these effects are partly mediated by modulation of sustained attention. A single-blinded, crossover, sham-controlled study was performed. Eighteen healthy right-handed participants performed cognitive tasks during three sessions of oppositional parietal tDCS stimulation: sham; right anodal with left cathodal (RA/LC); and right cathodal with left anodal (RC/LA). Participants performed a number comparison task, a modified Posner task, a choice reaction task (CRT) and the rapid visual processing task (RVP). RA/LC tDCS impaired number comparison performance compared with sham, with slower responses to numerically close numbers pairs. RA/LC and RC/LA tDCS had distinct effects on CRT performance, specifically affecting vigilance level during the final block of the task. No effect of stimulation on the Posner task or RVP was found. It was demonstrated that oppositional parietal tDCS affected both numerical performance and vigilance level in a polarity-dependent manner. The effect of tDCS on numerical processing may partly be due to attentional effects. The behavioural effects of tDCS were specifically observed under high task demands, demonstrating the consequences of an interaction between stimulation type and cognitive load.