A MEMS pressure sensor includes a resistive sensing bridge with a first sensing resistor and a second sensing resistor, each having variable resistance values in response to change in a sensed physical variable. An oscillator generates an oscillation signal with a frequency or period that is a function of an oscillator control signal. A sensor reference module generates the oscillator control signal as a function of the resistance value of a resistor coupled therewith. This sensor reference module is couplable with the first sensing resistor or second sensing resistor. A processing circuit coupled to the oscillator provides a sensor signal indicative of the frequency or period of the oscillation signal. The sensor signal has first and second values with the sensor reference module coupled with the first sensing resistor and with the second sensing resistor, respectively, the first and second values being thus jointly indicative of the physical variable sensed.