The k-Stirling permutations are a generalization of both ordinary permutations and Stirling permutations introduced by Gessel and Stanley. In this paper, we introduce the statistics “linv” and “lmaj” on k-Stirling permutations and prove that they are equidistributed. This generalizes the famous result of MacMahon that the permutation statistics inversion number and major index are equidistributed. Some further MacMahon type results for k-Stirling permutations are also given. As an application, we obtain a “peak-based” Mahonian permutation statistic. Moreover, we find three equidistributed bi-statistics on k-Stirling permutations, and call their common generating function the 1/k-Euler-Mahonian polynomial, which unifies the Eulerian, 1/k-Eulerian and Euler-Mahonian polynomials. The 1/k-Euler-Mahonian polynomial is a q-analogue of the 1/k-Eulerian polynomial, this solves a problem posed by Savage and Viswanathan.