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We propose to exploit rectification in field-effect transistors as an electrically controllable higher-order nonlinear phenomenon for the convenient monitoring of the temporal characteristics of THz pulses, for example, by autocorrelation measurements. This option arises because of the existence of a gate-bias-controlled super-linear response at sub-threshold operation conditions when the devices are subjected to THz radiation. We present measurements for different antenna-coupled transistor-based THz detectors (TeraFETs) employing (i) AlGaN/GaN high-electron-mobility and (ii) silicon CMOS field-effect transistors and show that the super-linear behavior in the sub-threshold bias regime is a universal phenomenon to be expected if the amplitude of the high-frequency voltage oscillations exceeds the thermal voltage. The effect is also employed as a tool for the direct determination of the speed of the intrinsic TeraFET response which allows us to avoid limitations set by the read-out circuitry. In particular, we show that the build-up time of the intrinsic rectification signal of a patch-antenna-coupled CMOS detector changes from 20 ps in the deep sub-threshold voltage regime to below 12 ps in the vicinity of the threshold voltage.