Nutrient inadequacies among picky-eaters have adverse effects on growth and development. Oral nutritional supplements (ONS) along with dietary counseling (DC), rather than DC alone as reported in our earlier publication, promoted growth among picky-eating Indian children aged from >24 m to ≤48 m with weight-for-height percentiles lying between the 5th and 25th (based on WHO Growth Standards) over 90 days. This paper presents the contribution of ONS to nutrient adequacy, dietary diversity, and food consumption patterns in children (N = 321). Weight, height, and dietary intakes, using 24-h food recalls, were measured at baseline (Day 1) and at Days 7, 30, 60, and 90. Nutrient adequacy, dietary diversity score (DDS), and food intake adequacy were calculated in both the supplementation groups (ONS1 + DC and ONS2 + DC; n = 107 in each group) and the control group (DC-only; n = 107). Supplements increased nutrient adequacy in both of the ONS + DC groups relative to control (p < 0.05). The proportions of children with adequate nutrient intakes increased significantly at Day 90 in the supplemented groups as compared to in the control group (p < 0.05), especially for total fat, calcium, vitamin A, vitamin C, and thiamin. Although no significant differences were observed in DDS in any of the groups, the percentage of children consuming ≥4 food groups in a day had increased in all the groups. Consumption of fruit and vegetables and cereals had increased significantly from baseline to Day 90. ONS along with dietary counseling was found to have improved nutritional adequacy without interfering with the normal food consumption patterns of picky-eating children at nutritional risk.