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.