Baldwin was born in Durham, Connecticut, in 1798, the second of twelve children. He studied at Williams College, graduated from Yale in 1821, and attended medical classes at Harvard — though he earned only a master of science degree, not a doctorate. Around 1826 he decided to become a missionary instead. After attending Auburn Theological Seminary and being ordained at Utica, New York, in 1830, he married Charlotte Fowler just three weeks before they sailed from New Bedford, Massachusetts, aboard the ship New England. They arrived in Hawaiʻi on June 21, 1831, part of the Fourth Company of the American Board of Commissioners for Foreign Missions. Their shipmate was Sheldon Dibble, who would later collaborate with David Malo on recording Hawaiian history. The two families — Baldwins and Alexanders, who arrived the following year — became lifelong friends, eventually intermarrying and forming a business partnership that would alter the islands forever.

Baldwin was first assigned to the mission at Waimea on the Big Island in 1832, then transferred in 1836 to Wainee Church in Lahaina, Maui's capital at the time. Since Lahaina was the seat of royal power, King Kamehameha III and Governor Hoapili attended his church. Baldwin translated a temperance tract into Hawaiian and helped Lorrin Andrews translate portions of the New Testament. His home at 696 Front Street became a hub for visiting scientists, including members of the United States Exploring Expedition. His library grew to over 200 volumes. But when epidemics struck in October 1848, Baldwin's biology coursework suddenly mattered more than his theology. The few trained physicians in the islands were in private practice in Honolulu, unreachable from Maui. For months, Baldwin was the only person with any Western medical knowledge available to the suffering population. He learned through brutal experience what worked in the remote tropical setting. Dartmouth College finally granted him an honorary medical degree in 1859, but the Hawaii medical association still refused him a license.

In 1855, the congregation of Wainee Church volunteered their labor under Baldwin's direction to construct a large building called Hale Aloha — "House of Love" — to commemorate having survived the epidemics. It was an act of communal memory, built by people who had watched their neighbors die and wanted to mark the fact that they had endured. Baldwin tried to retire in 1868, but was persuaded to help train native Hawaiian pastors at a Honolulu seminary instead. He taught there from 1872 to 1877, and served as a trustee of Oahu College, now Punahou School, from 1853 to 1875. He and Charlotte moved to Honolulu in 1870 as their health declined. Charlotte died in 1873; Dwight followed on January 3, 1886. They are buried at the Kawaiahaʻo Church cemetery.

The Baldwin name on Maui outlived the missionary by generations. His son Henry Perrine Baldwin co-founded Alexander & Baldwin with Samuel Thomas Alexander, building one of Hawaii's "Big Five" corporations that dominated the territory's economy into the twentieth century. Eldest son David Dwight Baldwin started Maui's first pineapple business. Daughter Harriet married Samuel Mills Damon, whose estate became one of the largest private landholders in the state. The family home on Front Street in Lahaina was deeded to the Lahaina Restoration Foundation in 1967 and operated as the Baldwin Home Museum — until August 8, 2023, when a massive wildfire destroyed it along with most of historic Lahaina. What the epidemics of 1848 could not erase, what a century and a half of change could not diminish, the fire consumed in hours. The museum is gone, but the story of the reluctant doctor from Connecticut remains woven into Maui's identity.