On the 25th of June, 1916, Thomas was born in Troy, New York, where he would later enlist in the US Army in October of 1940 at the age of 24. He was a Private when he deployed with the 105th Infantry Regiment, 27th Infantry Division to the Marianas Island and it was his actions there that would earn him the Medal of Honor. The citation reads:

For conspicuous gallantry and intrepidity at the risk of his life above and beyond the call of duty at Saipan, The Mariana Islands, 19 June to 7 July 1944. When his entire company was held up by fire from automatic weapons and small-arms fire from strongly fortified enemy positions that commanded the view of the company, Sgt. (then Pvt.) Baker voluntarily took a bazooka and dashed alone to within 100 yards of the enemy. Through heavy rifle and machine gun fire that was directed at him by the enemy, he knocked out the strong point, enabling his company to assault the ridge. Some days later while his company advanced across the open field flanked with obstructions and places of concealment for the enemy, Sgt. Baker again voluntarily took up a position in the rear to protect the company against a surprise attack and came upon two heavily fortified enemy pockets manned by two officers and ten enlisted men which had been bypassed. Without regard for such superior numbers, he unhesitatingly attacked and killed all of them. Five hundred yards farther, he discovered six men of the enemy who had concealed themselves behind our lines and destroyed all of them. On 7 July 1944, the perimeter of which Sgt. Baker was a part was attacked from 3 sides by from 3,000 to 5,000 Japanese. During the early stages of this attack, Sgt. Baker was severely wounded, but he insisted on remaining in the line and fired at the enemy at ranges sometimes as close as 5 yards until his ammunition ran out. Without ammunition and with his weapon battered to uselessness from hand-to-hand combat, he was carried about 50 yards to the rear by a comrade, who was then himself wounded. At this point Sgt. Baker refused to be moved any further stating that he preferred to be left to die rather than risk the lives of any more of his friends. A short time later, at his request, he was placed in a sitting position against a small tree. Another comrade, withdrawing, offered assistance. Sgt. Baker refused, insisting that he be left alone and be given a soldier's pistol with its remaining eight rounds of ammunition. When last seen alive, Sgt. Baker was propped against a tree, pistol in hand, calmly facing the foe. Later Sgt. Baker's body was found in the same position, gun empty, with 8 Japanese lying dead before him. His deeds were in keeping with the highest traditions of the U.S. Army.

Thomas was posthumously promoted to the rank of Sergeant and received the Medal of Honor. Thomas Alexander Baker is buried in the Gerald G.H. Solomon Saratoga National Cemetery in Schuylerville, New York: Section F, Grave 162.