Smartphones are frequently involved in accessing private user data. Although many studies have been done to prevent malicious apps from leaking private user data, only a few recent works examine how to remove the sensitive information from the data collected by smartphone hardware resources (e.g., camera). Unfortunately, none of them investigates whether a malicious app can obtain such sensitive information when (or right before/after) a legitimate app collects such data (e.g., taking photos). To fill in the gap, in this paper, we model such attacks as the Resource Race Attack (RRAttack) based on races between two apps during their requests to exclusive resources to access sensitive information. RRAttacks have three categories according to when a race on requesting resources occurs: Pre-Use, In-Use, and Post-Use attacks. We further conduct the first systematic study on the feasibility of launching the RRAttacks on two heavily used exclusive Android resources: camera and touchscreen. In details, we perform Proof-of-Concept (PoC) attacks to reveal that, (a) camera is highly vulnerable to both In-Use and Post-Use attacks; and (b) touchscreen is vulnerable to Pre-Use attacks. Particularly, we demonstrate successful RRAttacks on them to steal private information, to cause financial loss, and to steal user passwords from Android 6 to the latest Android Q. Moreover, our analyses on 1,000 apps indicate that most of them are vulnerable to one to three RRAttacks. Finally, we propose a set of defense strategies against RRAttacks for user apps, system apps, and Android system itself.