The triacylglycerol (TAG) profiles present in real world lipidic samples are usually quite complex and, as such, monodimensional high-performance liquid chromatographic (HPLC) techniques are inadequate when challenged with such matrices. In this respect, the complementary use of silver-ion (Ag) and non-aqueous (NA) reversed-phase (RP) HPLC can be exploited if thorough TAG separations are required. The present investigation reports the employment of a newly developed comprehensive LC (LC × LC) system, based on the different separation mechanisms of the aforementioned techniques, and applied to a rice oil sample. The approach was successful in the separation of a high number of solutes, otherwise unachievable through monodimensional LC. Furthermore, the use of atmospheric pressure chemical ionization mass spectrometry (APCI-MS), as detection system, provided a third analytical dimension boosting the identification power of the comprehensive chromatographic method.