The mechanism of human immunodeficiency virus 1 (HIV-1) nuclear entry, required for productive infection, is not fully understood. Here, we report that in HeLa cells and activated CD4+ T cells infected with HIV-1 pseudotyped with VSV-G and native Env protein, respectively, Rab7+ late endosomes containing endocytosed HIV-1 promote the formation of nuclear envelope invaginations (NEIs) by a molecular mechanism involving the VOR complex, composed of the outer nuclear membrane protein VAP-A, hyperphosphorylated ORP3 and Rab7. Silencing VAP-A or ORP3 and drug-mediated impairment of Rab7 binding to ORP3-VAP-A inhibited the nuclear transfer of the HIV-1 components and productive infection. In HIV-1-resistant quiescent CD4+ T cells, ORP3 was not hyperphosphorylated and neither VOR complex nor NEIs were formed. This new cellular pathway and its molecular players are potential therapeutic targets, perhaps shared by other viruses that require nuclear entry to complete their life cycle.