Allosteric integrase (IN) inhibitors (ALLINIs), which are promising preclinical compounds that engage the lens epithelium-derived growth factor (LEDGF)/p75 binding site on IN, can inhibit different aspects of human immunodeficiency virus 1 (HIV-1) replication. During the late phase of replication, ALLINIs induce aberrant IN hyper-multimerization, the consequences of which disrupt IN binding to genomic RNA and virus particle morphogenesis. During the early phase of infection, ALLINIs can suppress HIV-1 integration into host genes, which is also observed in LEDGF/p75-depelted cells. Despite this similarity, the roles of LEDGF/p75 and its paralog hepatoma-derived growth factor like 2 (HDGFL2) in ALLINI-mediated integration retargeting are untested. Herein, we mapped integration sites in cells knocked out for LEDGF/p75, HDGFL2, or both factors, which revealed that these two proteins in large part account for ALLINI-mediated integration retargeting during the early phase of infection. We also determined that ALLINI-treated viruses are defective during the subsequent round of infection for integration into genes associated with speckle-associated domains, which are naturally highly targeted for HIV-1 integration. Class II IN mutant viruses with alterations distal from the LEDGF/p75 binding site moreover shared this integration retargeting phenotype. Altogether, our findings help to inform the molecular bases and consequences of ALLINI action.