Size dependent three-photon absorption (3PA) and three-photon-excited photoluminescence (PL) of CdSe/CdS nanorod heterostructures have been investigated using Z-scan and upconversion PL techniques with 150-fs laser pulses at 1300 nm. The PL from these rods show clear cubic power dependence and the 3PA cross-section (σ3) was found to be as high as 1.5×10^(-75) cm^6s^2photon^(-2) for 39 nm long rods, which is two to four orders of magnitude larger than those previously reported for spherical semiconductor nanocrystals (NCs) under ~100 fs laser pulse excitation. Importantly, by exploiting the unique property of the seeded nanorods to exhibit strong quantum confinement even at relatively large rod sizes, a superlinear dependence of the 3PA cross-section on nanoparticle volume was found and validated over a wide volume range. A simple derived relation that quantitatively describes σ3 and takes into account the laser pulse duration, is proposed; thereby providing a clear basis of comparison between the σ3 values of various II-VI semiconductor nanomaterials and facilitating a more judicious choice of their use in 3PA applications.