Differential scanning calorimetry at an elevated external pressure (Pressure DSC) allows for shifting the vaporization of a sample to higher temperatures, thus often facilitating the direct observation of its thermal decomposition. In the present work, the thermolysis of a promising energetic material 3,5-dinitropyrazole was studied under pressures up to 10 MPa. The thermokinetic analysis of the datasets acquired at 2 and 5 MPa exhibited a pronounced kinetic compensation, thus allowing to build the joint formal kinetic model. The final kinetic scheme is comprised of the two parallel reactions, viz., the first-order process (Ea = 198 kJ mol−1) along with a first-order autocatalysis (Ea = 127 kJ mol−1). The experiment was complemented with the highly accurate CCSD(T)-F12 quantum chemical calculations. Theory revealed an unusual primary decomposition channel, viz., a sigmatropic [1,5]H-shift followed by the pyrazole ring opening yielding a molecular nitrogen and a nitro radical as simple primary products. Apart from this, the comparative thermogravimetry at a normal pressure yielded the vapor pressure of 3,5-dinitropyrazole along with the internally consistent set of phase change enthalpies. In general, the pressure DSC is a facile technique to study the true decomposition kinetics of the compounds that vaporize/sublime in conventional DSC experiments.