This study investigated whether the supplementation of prebiotic inulin to gestating sows programmatically affects offspring growth performance and meat quality while exploring its epigenetic effects through histone acetylation modulation. After mating, sixty multiparous sows (Landrace × Yorkshire; parity 2–3) were assigned to a 2 × 2 factorial arrangement with inulin (0% vs. 1.5%) and fat (0% or 5%) supplementation until farrowing. Post-weaning, five litters (10 piglets per litter) per treatment were selected and maintained in their original litter for fattening under standardized feeding. The results demonstrated that maternal inulin supplementation during gestation accomplished the following: (1) Increased offspring liver index by 13.4% at weaning and 6.8% at finishing (p < 0.05) while reducing the finishing-phase backfat thickness by 11.6% (p < 0.01), with a significant inulin × fat interaction attenuating fat-induced abdominal lipid accumulation at weaning (p = 0.05). (2) Decreased longissimus dorsi muscle lightness (L*) by 4.5% in finishing pigs (p = 0.02) without altering the other meat quality parameters. (3) Suppressed offspring liver lipid deposition at birth and finishing (p < 0.05), concomitant with upregulated hepatic PGC-1α and CPT1A expression (p < 0.05). (4) Elevated neonatal serum butyrate by 15.6% (p = 0.06) while inhibiting hepatic histone deacetylase (HDAC) activity and enhancing histone H3/H4 acetylation (p < 0.01). These findings suggest that maternal inulin supplementation during gestation mitigates offspring hepatic lipid deposition through butyrate-mediated epigenetic regulation, where microbial-derived butyrate from inulin fermentation inhibits HDAC activity, enhances histone acetylation levels, and upregulates fatty acid β-oxidation gene expression. This study provides novel mechanistic insights into how maternal dietary fiber nutrition programs offspring development through epigenetic reprogramming.