Quasi-low-dimensional type II superconductors in parallel magnetic fields are studied when singlet pairing interactions and relatively weak triplet pairing interactions coexist. Singlet and triplet components of order parameter are mixed at high fields, and at the same time an inhomogeneous superconducting state called a Fulde-Ferrell-Larkin-Ovchinnikov state occurs. As a result, the triplet pairing interactions enhance the upper critical field of superconductivity remarkably even at temperatures far above the transition temperature of parallel spin pairing. It is found that the enhancement is very large even when the triplet pairing interactions are so weak that a high field phase of parallel spin pairing may not be observed in practice. A possible relvance of the result in organic superconductors and a hybrid-ruthenate-cuprate superconductor is discussed.