Sweet potato (Ipomoea batatas (L.) Lam.) is one of the most widely cultivated crops in the world, with outstanding stress tolerance, but drought stress can lead to a significant decrease in its yield. To reveal the response mechanism of sweet potato to drought stress, an integrated physiological, transcriptome and metabolome investigations were conducted in the leaves of two sweet potato varieties, drought-tolerant zhenghong23 (Z23) and a more sensitive variety, jinong432 (J432). The results for the physiological indexes of drought showed that the peroxidase (POD) and superoxide dismutase (SOD) activities of Z23 were 3.68 and 1.21 times higher than those of J432 under severe drought, while Z23 had a higher antioxidant capacity. Transcriptome and metabolome analysis showed the importance of the amino acid metabolism, respiratory metabolism, and antioxidant systems in drought tolerance. In Z23, amino acids such as asparagine participated in energy production during drought by providing substrates for the citrate cycle (TCA cycle) and glycolysis (EMP). A stronger respiratory metabolism ability could better maintain the energy supply level under drought stress. Drought stress also activated the expression of the genes encoding to antioxidant enzymes and the biosynthesis of flavonoids such as rutin, resulting in improved tolerance to drought. This study provides new insights into the molecular mechanisms of drought tolerance in sweet potato.