As your wording correctly indicates, Lincoln initially did not wish to interfere with slavery in the states where it already existed. Though he was explicitly opposed to the institution, he believed that immediate abolition would simply create too much disorder in the southern states. By excluding it from the territories—the areas of the U.S. that had not yet been organized into states—Lincoln believed that slavery would eventually die a natural death. His intention at the start was to attempt ending the rebellion quickly and to bring the seceded states back into the Union with as little disruption as possible to southern society.

Obviously this didn't happen. As early as First Bull Run (Manassas) in July of 1861, with the rout of Union forces and their headlong retreat to Washington, it became clear that the rebellion couldn't be put down quickly and with little bloodshed. Over the next year each development confirmed that the war would be long and protracted. Though Union progress was being made in the western theater (despite huge casualties at Shiloh in April, '62), in the east this wasn't the case. Union defeats, with thousands of dead and wounded on both sides, occurred in the Seven Days' battles outside Richmond in June and July of 1862 and at Second Bull Run in August. Lincoln and his administration realized a fundamental change had to be made in the actual goals of the war if the Union was to be successful. The emancipation of the enslaved people was to be the cornerstone of this new objective.

It's cynical, and simply false as well, to view this change entirely as a desperate measure Lincoln carried out because the war was going badly. This was part of his motivation, admittedly, but Lincoln's understanding of the issues was evolving independently of events on the battlefields. As a result of study, of introspection, and of the persistent lobbying efforts of abolitionists such as Frederick Douglass and others, Lincoln's intentions were gradually transformed. In addition, the enslaved people had also effectively begun liberating themselves, fleeing by the thousands across the Union lines. Southern society already had been disrupted, and massively so. In order to forestall the criticism (which was leveled at him anyway by the South and its apologists, and still is in some quarters today) that he was doing so merely because he was losing the war, Lincoln waited until after the quasi-victory of Antietam in September, 1862 to issue his preliminary emancipation measure. When it was officially proclaimed in January, emancipation (though at this point unfortunately only in the areas "in rebellion") accomplished the following things immediately:

1) African American men could now be recruited in large numbers into the Union armed forces and thus aid the cause of liberation.

2) It made recognition of the Confederacy by the European countries that had previously been sympathetic to it, Britain and France, impossible. Now that abolition was an explicit goal of the war, it would have been an embarrassment to those countries, with their humanitarian pretensions, to be enemies of the side that sought to end slavery.

3) There was now no longer a disconnect between Lincoln's philosophy, which had always been anti-slavery, and the manner in which the war was to be prosecuted.

When the new nation "conceived in liberty" had been founded "four score and seven" years earlier, slavery had been a blot on its ideals and its very existence. The Founders who declared independence, including those like Jefferson who were practitioners of it, knew that slavery was wrong. They failed to enact abolition in 1776 (though the northern states did pass gradual emancipation laws in the wake of the Revolution) for the same reason that Lincoln wanted to avoid it 85 years later, in 1861: the assumption that it would create chaos. Lincoln finally took the decisive step to remove this stain from the United States—partly because it was necessary for military and diplomatic reasons, and partly because the step was in accordance with the principle of freedom for all in which he already believed, but so far had failed to act on.

At first, when the Civil War broke out in 1861, Lincoln wanted only to preserve the Union and bring the southern states that had seceded back into the Union. His premise at the outset of the war was that the Confederate states had no right to secede, that their actions were traitorous, and that the Union was justified in trying to bring the Confederacy back into the nation.

However, as the Union Army began fighting, Lincoln realized that the war would be difficult to win. It became necessary for him to provide a rationale grounded in democracy to motivate the Union troops and the North and to provide a broader context for fighting the war. In 1862, he signed the Emancipation Proclamation, which took effect in 1863 and freed the slaves in the Confederacy. Though this was largely a symbolic action, it signified Lincoln's eventual commitment to ending slavery and providing a more meaningful rationale for fighting the deadly and long Civil War. 

In addition, Lincoln knew that by supporting the abolition of slavery, he would make it difficult for European powers such as England to support the Confederacy. This is because there was a strong abolitionist sentiment in England. 

At the outbreak of the Civil War, Lincoln declared that his main goal was the preservation of the Union and not the freedom of slaves. After the first few terrible years of the war, his views on the goals had changed.

Originally Lincoln has seen the send of slavery and the preservation of the Union as two different goals. He once said, “If I could preserve the Union and not free a single slave, I would do it. If I could preserve the Union and free them all, I would do that.”

By 1862, he realized that ending slavery would actually help him win the Civil War. First, it would deprive the south of European support. If the war were re-defined as a war against slavery, European nations could no longer support the south in good conscious. Also, slaves would be empowered to run away, rebel or maybe join the Union army. Lincoln’s abolitionist advisors expected that African Americans would sign up by the battalion if the wars goals were aimed towards freeing their fellow slaves in the south.

So Lincoln didn’t shift his beliefs so much, he just finally realized that both aims complimented each other and helped his ultimate goal.