Recent discovery of spin-polarized single-Dirac-cone insulators, whose variants can host magnetism and superconductivity, has generated widespread research activity in condensed-matter and materials-physics communities. Some of the most interesting topological phenomena, however, require topological insulators to be placed in multiply connected, highly constrained geometries with magnets and superconductors, all of which thus require a large number of functional variants with materials design flexibility as well as electronic, magnetic and superconducting tunability. Given the optimum materials, topological properties open up new vistas in spintronics, quantum computing and fundamental physics. We have extended the search for topological insulators from the binary Bi-based series to the ternary thermoelectric Heusler compounds. Here we show that, although a large majority of the well-known Heuslers such as TiNiSn and LuNiBi are rather topologically trivial, the distorted LnPtSb-type (such as LnPtBi or LnPdBi, Ln = f(n) lanthanides) compounds belonging to the half-Heusler subclass harbour Z(2) = -1 topological insulator parent states, where Z(2) is the band purity product index. Our results suggest that half-Heuslers provide a new platform for deriving a host of topologically exotic compounds and their nanoscale or thin-film device versions through the inherent flexibility of their lattice parameter, spin-orbit strength and magnetic moment tunability paving the way for the realization of multifunctional topological devices.