Then-President Franklin D. Roosevelt traveled, mainly by ship, from Washington to Tehran to meet with British Prime Minister Winston Churchill and Russian General Secretary Joseph Stalin, he told "Tucker Carlson Tonight" on Monday.
"The Allies were literally at the brink -- they could have lost World War II," he said.
"Hitler is on the march in Europe, the U.S. has had minor success in the Pacific against the Japanese, but that could go the other way, too."
Baier said his book tells how Stalin agreed to the meeting but only if it took place in the Soviet embassy in Tehran, Iran.
In that event, Roosevelt embarked on the long journey after he and Churchill realized they needed Moscow's help to defeat the Nazis.
"There's a chance, though, in FDR's mind that Stalin could go the other way and side with Hitler," he said.
"Then, the war is off."
However, the three leaders finally met at the Tehran Conference and planned Operation Overlord, which later became known as the D-Day invasion of German-occupied France.
"That changed the war -- that changed the world," Baier said.
During the interview, he also told host Tucker Carlson of a close call involving friendly fire that could have been a disaster for the U.S.
With Roosevelt and several joint chiefs of staff aboard the USS Iowa -- which was chaperoned across the sea by several other American ships -- the USS William D. Porter accidentally fired a live torpedo in the Iowa's direction while simulating a military exercise to show the then-president the ships' capabilities, Baier said.
Thanks to an expert response by the Iowa's crew, the missile reportedly missed the hull and instead exploded about 1,000 feet off in the ship's wake.