We experimentally investigated the asymmetric dual-grating-gate plasmonic terahertz (THz) detector based on an InGaAs-channel high-electron-mobility transistor (HEMT) in the gate-readout configuration. Throughout the THz pulse detection measurement on the fabricated device, we discovered a new detection mechanism called the “3D rectification effect” at the positive gate bias application, which is a cooperative effect of the plasmonic nonlinearities in the channel with the diode nonlinearity in the heterobarrier between the InGaAs channel layer and the InAlAs spacer/carrier-supply/barrier layers, resulting in a giant enhancement of the detector responsivity. We also found that an undesired long-tail waveform observed on the temporal pulse photoresponse of the device is due to trapping of carriers to the donor levels in the silicon δ-doped carrier-supply layer when they tunnel through the barrier to the gate and can be eliminated completely by introducing the so-called inverted-HEMT structure. The internal current responsivity and noise-equivalent power are estimated to be 0.49 A/W (with the equivalent voltage responsivity of 4.9 kV/W with a high output impedance of 10 kΩ) and 196 pW/√Hz at 0.8 THz. These results pave the way towards the application of the plasmonic THz detectors to beyond-5G THz wireless communication systems.