Randomness, mainly in the form of random numbers, is the fundamental prerequisite for the security of many cryptographic tasks. Quantum randomness can be extracted even if adversaries are fully aware of the protocol and even control the randomness source. However, an adversary can further manipulate the randomness via tailored detector blinding attacks, which are hacking attacks suffered by protocols with trusted detectors. Here, by treating no-click events as valid events, we propose a quantum random number generation protocol that can simultaneously address source vulnerability and ferocious tailored detector blinding attacks. The method can be extended to high-dimensional random number generation. We experimentally demonstrate the ability of our protocol to generate random numbers for two-dimensional measurement with a generation speed of 0.1 bit per pulse.