Artificial intelligence (AI) has become the infrastructural logic of social commerce, where algorithmic recommenders mediate what consumers see, trust and buy. Yet evidence on how AI-enabled recommendations translate into engagement and purchase behaviour inside socially embedded shopping environments remains fragmented. Drawing on the stimulus–organism–response (S-O-R) framework and integrating trust and privacy-calculus reasoning, this study develops and tests a model linking AI recommendation quality and perceived personalisation to consumer engagement and purchase intention. A structurally calibrated dataset of 420 social commerce users was analysed using standardised OLS regression, bootstrapped mediation with 5,000 resamples and moderated regression. AI recommendation quality (β = .228, p < .001) and trust in AI recommendations (β = .349, p < .001) significantly drove consumer engagement (R² = .344), while engagement was the strongest predictor of purchase intention (β = .383, p < .001; R² = .436). Trust transmitted a significant indirect effect from recommendation quality to purchase intention (β = .196, 95% CI [.147, .251]) and perceived personalisation transmitted a significant indirect effect through engagement (β = .196, 95% CI [.142, .255]); trust also influenced purchase intention indirectly through engagement (β = .216, 95% CI [.159, .281]). Privacy concern did not significantly moderate the personalisation–trust link (ΔR² = .006, p = .075), although the interaction was directionally negative. The findings position trust and engagement as the principal conduits through which algorithmic recommendation creates commercial value, and caution that personalisation alone is insufficient without trust-building.