To help diagnose and initiate antiretroviral therapy (ART) for ≥95% of all persons living with HIV (PLHIV), the World Health Organization (WHO) recommends offering HIV testing to biological children, and sexual and needle-sharing partners of all PLHIV (index-client testing, ICT). Many index clients, however, do not identify or have contactable partners, and often substantially fewer than 95% of HIV-positive partners initiate ART soon after index testing. To help improve early HIV diagnosis and ART initiation in Eswatini (formerly Swaziland), we implemented a community-based HIV testing and peer-delivered, linkage case management program (CommLink) that provided ICT as part of a comprehensive package of WHO recommended linkage services. CommLink was implemented June 2015 –March 2017 (Phase I), and April 2017 –September 2018 (Phase II). In addition to biological children and partners, HIV testing was offered to adult family members (Phases I and II) and high-risk associates including friends and acquaintances (Phase II) of CommLink index clients. Compared with Phase I, in Phase II proportionally more CommLink clients disclosed their HIV-infection status to a partner or family member [94% (562/598) vs. 75% (486/652)], and had ≥1 partners, family members, or high-risk associates (contacts) tested through CommLink [41% (245/598) vs. 18% (117/652)]. Of 537 contacts tested, 253 (47%) were HIV-positive and not currently in HIV care, including 17% (17/100) of family members aged <15 years, 42% (78/187) of non-partner family members aged ≥15 years, 60% (73/121) of sexual partners, and 66% (85/129) of high-risk associates. Among 210 HIV-positive contacts aged ≥15 years who participated in CommLink, nearly all received recommended linkage services including treatment navigation (95%), weekly telephone follow-up (93%), and ≥3 counseling sessions (94%); peer counselors resolved 76% (306/404) of identified barriers to care (e.g., perceived wellness); and 200 (95%) initiated ART at a healthcare facility, of whom 196 (98%) received at least one antiretroviral refill before case-management services ended. To help countries achieve ≥90% ART coverage among all PLHIV, expanding ICT for adult family members and high-risk associates of index clients, and providing peer-delivered linkage case management for all identified PLHIV, should be considered.