A first-order magnetoelastic transition (FOMT) is found near the triple point between ferromagnetic, antiferromagnetic and paramagnetic phases in the magneto-chemical phase diagram of (Hf1-xNbx)Fe2 Laves phase system. We show that bringing different magnetic states to the edge of stability, both as a function of the chemical composition and under the influence of external stimuli, such as temperature, pressure and magnetic field, is essential to obtain and control FOMTs. Temperature dependent X-ray diffraction experiments reveal a discontinuity in the lattice parameter a and the unit cell volume without the change in the crystal symmetry at the FOMT. Under applied pressure, the transition temperature drastically shifts downward at a remarkable rate of −122 K/GPa. It is this first-order magnetic transition that leads to a negative thermal expansion (NTE) with average ΔV/(VΔT) ≈ −15 × 10−6 K−1 observed over a 90 K broad temperature range, which is uncommon for magnetoelastic NTE materials. Density functional theory calculations and microstructural analyses demonstrate that the unusual broadness of the FOMT originates from phase separation between ferro- and antiferromagnetic phases, which in turn is rooted in partial segregation of Hf and Nb and a peculiar microstructure. This new understanding of the composition-structure-property relationships in transition metal based Laves phases is an essential step toward a better control and more precise tailoring of rich functionalities in this group of material.