Cognitive functioning is known to be impaired following sleep deprivation and to fluctuate depending on the time of day. However, most methods of assessing cognitive performance remain impractical for environments outside of the lab. This study investigated whether 2-min smartphone-based versions of commonly used cognitive tests could be used to assess the effects of sleep deprivation and time of day on diverse cognitive functions. After three nights of normal sleep, participants (N = 182) were randomised to either one night of sleep deprivation or a fourth night of normal sleep. Using the Karolinska WakeApp (KWA), participants completed a battery of 2-min cognitive tests, including measures of attention, arithmetic ability, episodic memory, working memory, and a Stroop test for cognitive conflict and behavioural adjustment. A baseline measurement was completed at 22:30 h, followed by three measurements the following day at approximately 08:00 h, 12:30 h, and 16:30 h. Sleep deprivation led to performance impairments in attention, arithmetic ability, episodic memory, and working memory. No effect of sleep deprivation was observed in the Stroop test. There were variations in attention and arithmetic test performance across different times of day. The effect of sleep deprivation on all cognitive tests was also found to vary at different times of day. In conclusion, this study shows that the KWA’s 2-min cognitive tests can be used to detect cognitive impairments following sleep deprivation, and fluctuations in cognitive performance relating to time of day. The results demonstrate the potential of using brief smartphone-based tasks to measure a variety of cognitive abilities within sleep and fatigue research.