Background: Antimicrobial resistance (AMR) threatens neonatal survival in low-resource settings, yet the contribution of health system factors—infrastructure, staffing, guidelines, laboratory capacity, and healthcare worker (HCW) training—to AMR management outcomes remains poorly characterized. Methods: This was a multicentre quasi-experimental study across six hospitals (three intervention and three control) in Kiambu County. The AMS intervention comprised clinical guidelines, HCW training, audit-and-feedback, and laboratory strengthening with 214 neonates (105 intervention, 109 comparison) enrolled and 154 HCWs. Outcomes included appropriate prescribing, guideline adherence, empiric-to-target switch, multidrug-resistant (MDR) organism isolation, mortality, and length of stay. Results: Pre-post improvements were significant for all stewardship outcomes (McNemar χ2 range 66–71, all p < 0.001) and mortality (χ2 ≈ 18.0, p < 0.001). Between-group differences favoured the intervention arm for appropriate prescribing (81.2% vs 64.9%, χ2 = 7.32, p = 0.007, V = 0.186), guideline adherence (75.2% vs 60.8%, p = 0.034), and empiric-to-target switch (68.4% vs 52.6%, p = 0.026). Culture-before-therapy was strongly associated with MDR isolation (OR = 3.70, 95% CI 1.82–7.51, p < 0.001), reflecting detection bias. Guideline adherence predicted appropriate prescribing (OR = 2.94, 95% CI 1.56–5.52, p = 0.001). Empiric-to-target switch predicted survival (OR = 2.67, 95% CI 1.31–5.47, p = 0.007). Conclusion: Health system factors—particularly guideline availability, laboratory capacity, and HCW training—are modifiable determinants of AMS outcomes. Strengthening these system-level pillars is essential for containing AMR in neonatal sepsis across Kenyan county hospitals.