We introduce a setting that we call Device-Enhanced PAKE (DEPAKE), where PAKE (password-authenticated key exchange) protocols are strengthened against online and offline attacks through the use of an auxiliary device that aids the user in the authentication process. We build such schemes and show that their security, properly formalized, achieves maximal-attainable resistance to online and offline attacks in both PKI and PKI-free settings. In particular, an online attacker must guess the user's password and also corrupt the user's auxiliary device to authenticate, while an attacker who corrupts the server cannot learn the users' passwords via an offline dictionary attack. Notably, our solutions do not require secure channels, and nothing (in an information-theoretic sense) is learned about the password by the device (or a malicious software running on the device) or over the device-client channel, even without any external protection of this channel. An attacker taking over the device still requires a full online attack to impersonate the user. Importantly, our DE-PAKE scheme can be deployed at the user end without the need to modify the server and without the server having to be aware that the user is using a DE-PAKE scheme. In particular, the schemes can work with standard servers running the usual password-over-TLS authentication. We use these protocols to implement a practical DE-PAKE system and we evaluate its performance. To improve usability the implemented system utilizes automated and user-transparent data channel between the mobile device and the client, falling back to localized communication if the device looses primary connectivity.