What you are missing are two things, (a) that the ESD spike is typically produced by a small capacitor (industrially-accepted "human body" model is 100pF) and therefore is short (100 ns typical), and (b) that any power supply rails have substantial bypass capacitors attached (at least 100,000 pF and much more). So in case of ESD spike the short-lasting charge gets easily "absorbed" by those capacitors without noticeable increase in Vcc.
In fact, the 0.1uF caps are strongly recommended to place in closest proximity to ESD protective diodes.
If you mean how to protect an input from long sustained overvoltage, then the signal path should have a sort of switchable voltage divider. An example would be this US patent, where a N-MOS transistor essentially disconnects the input when it goes above the gate threshold voltage.