(FORTUNE Magazine) - At the 1860 Republican National Convention, a lawyer with only a single term in Congress to his political credit beat three seasoned politicians for the nomination. Once Abraham Lincoln won the presidency he asked his rivals to join his administration--a decision at the heart of Doris Kearns Goodwin's book, Team of Rivals: The Political Genius of Abraham Lincoln.

FORTUNE's Jia Lynn Yang asked Goodwin how Lincoln did it.

FORTUNE: What was Lincoln thinking?

Doris Kearns Goodwin: Most presidents in previous decades picked supporters to be in the cabinet. Lincoln takes the opposite approach. He is saying, in effect, "These three rivals are the strongest men in the country. I have no right to deprive it of their services." William Seward, who became Secretary of State, had been a governor and senator in New York. Salmon Chase, later Lincoln's Treasury secretary, was governor of Ohio. And Edward Bates, appointed attorney general, was an accomplished judge. Lincoln thought it was worth having the best talent.

FORTUNE: So how did he win them over?

DKG: Lincoln had such sensitive antennae. He understood how to share credit and how to shoulder blame. He knew how to use humor. We know so much about his management style because of the letters he would write. When he was angry with one of them, he had this tendency of writing what he called a hot letter. Then he would put it aside, waiting for his emotions to cool down, and never send it.

FORTUNE: How did Lincoln manage these egos--including his own?

DKG: That's absolutely the great mystery of Lincoln. He had a deep self-confidence. But on the other hand he didn't allow his short-term ego to get in the way. He always had the larger goal in front of him. He thought, "I can deal with any of these old grudges as long as I feel we are pulling together to accomplish the goal of eventually saving the Union and emancipating the slaves."