Murray's 7-5, 4-6, 6-2, 7-5 victory Sunday at the Rio Games makes him the first man or woman with two Olympic singles titles, let alone two in a row.
At London in 2012, Murray won a singles gold and mixed doubles silver.
The second-seeded Murray stretched his winning streak to a career-high 18 matches and stopped the resurgent run of the 141st-ranked del Potro, who knocked off No. 1 Novak Djokovic in the first round and No. 3 Rafael Nadal in the semifinals.
Del Potro's silver goes alongside his bronze from four years ago.
Kei Nishikori defeated Nadal for the bronze earlier Sunday.