Promotion came slowly, and he was still a captain on this date in 1862, in the middle of the two-day Battle of Fort Pulaski. (Wikipedia, which is usually pretty good, errs in dating his promotion to brigadier general before the battle, as can be seen here and here.)
Despite Gillmore's relatively junior rank, his siege guns and engineering expertise played the key role in the victory, forcing the Confederates to surrender on April 11. The battle enabled the Navy to enforce the blockade of Savannah for the rest of the war (or rather until Sherman captured the city before Christmas in 1864).
Just under a year after Fort Pulaski, in his first independent command, Brig.-Gen. Gillmore defeated Confederate raiders at the Battle (or skirmish) of Somerset, Kentucky.
Promoted to major general and command of the Department of the South, Gillmore launched two costly and unsuccessful assaults on Fort Wagner near Charleston in July 1863. Reverting to siege warfare, he captured the fort in September. Like many others he feuded with Maj.-Gen. Ben Butler, and his wartime service petered out.
Gillmore's son and grandson were career officers in the US Army, and his great-grandson served in World War II.