Sleep is critical to human function, mediating factors like memory, mood, energy, and alertness; therefore, it is commonly conjectured that a good night's sleep is important for job performance. However, both real-world sleep behavior and job performance are hard to measure at scale. In this work, we show that people's everyday interactions with online mobile apps can reveal insights into their job performance in real-world contexts. We present an observational study in which we objectively tracked the sleep behavior and job performance of salespeople (N = 15) and athletes (N = 19) for 18 months, using a mattress sensor and online mobile app. We first demonstrate that cumulative sleep measures are correlated with job performance metrics, showing that an hour of daily sleep loss for a week was associated with a 9.0% and 9.5% reduction in performance of salespeople and athletes, respectively. We then examine the utility of online app interaction time as a passively collectible and scalable performance indicator. We show that app interaction time is correlated with the performance of the athletes, but not the salespeople. To support that our app-based performance indicator captures meaningful variation in psychomotor function and is robust against potential confounds, we conducted a second study to evaluate the relationship between sleep behavior and app interaction time in a cohort of 274 participants. Using a generalized additive model to control for per-participant random effects, we demonstrate that participants who lost one hour of daily sleep for a week exhibited 5.0% slower app interaction times. We also find that app interaction time exhibits meaningful chronobiologically consistent correlations with sleep history, time awake, and circadian rhythms. Our findings reveal an opportunity for online app developers to generate new insights regarding cognition and productivity.