Nutrient management is important for enhancing crop productivity economically, as well as for environmental protection. The present study explored the best relative ratio of potassium (K) to nitrogen (N) under a new short-season, high-density planting model, based on the sucrose metabolism in the subtending leaves of cotton in relation to yield. A 2-year (2016–2017) field experiment was conducted in a randomized complete block design along with four replicates. The treatments were three K relative ratios to N [K08 {K (K2O): N = 0.8:1 (168:210 kg ha−1)}, K10 {K (K2O): N = 1:1 (210:210 kg ha−1)}, and K12 {K (K2O): N = 1.2:1 (252:210 kg ha−1)}]. The plot size was 36.48 m2 comprised of four rows. Plants were sown on raised beds. Row spacing was managed to 0.76 m with a plant-to-plant distance of 0.14 m to maintain a planting density of 9 plants m−2. The results indicated that increased K application ratios substantially favored sucrose metabolism in the subtending leaves to attain higher cotton yields. K10 and K12 upregulated the photosynthetic rate (Pn) of subtending leaves by 17–32% and 33–59%, sucrose phosphate synthase activities by 4–17% and 14–28%, and sucrose synthase activities by 12–25% and 21–36%, respectively. Glucose-6-phosphate dehydrogenase and soluble acid invertase activities were significantly downregulated. K10 improved seed and lint yield by 10–24% with no differences between K10 and K12, suggesting K10 (K2O: N; 1:1) to be the best ratio for cost-effective cotton production under the new planting model in the Yangtze River Valley, China.