Molecular evolution is often conceptualised as adaptive walks on rugged fitness landscapes, driven by mutations and constrained by incremental fitness selection. It is well known that epistasis shapes the ruggedness of the landscape’s surface, outlining their topography (with high-fitness peaks separated by valleys of lower fitness genotypes). However, within the strong selection weak mutation (SSWM) limit, once an adaptive walk reaches a local peak, natural selection restricts passage through downstream paths and hampers any possibility of reaching higher fitness values. Here, in addition to the widely used point mutations, we introduce a minimal model of sequence inversions to simulate adaptive walks. We use the well known NK model to instantiate rugged landscapes. We show that adaptive walks can reach higher fitness values through inversion mutations, which, compared to point mutations, allows the evolutionary process to escape local fitness peaks. To elucidate the effects of this chromosomal rearrangement, we use a graph-theoretical representation of accessible mutants and show how new evolutionary paths are uncovered. The present model suggests a simple mechanistic rationale to analyse escapes from local fitness peaks in molecular evolution driven by (intragenic) structural inversions and reveals some consequences of the limits of point mutations for simulations of molecular evolution.