Well there are a variety of reasons but most can boil down to nationalism and sense of country. While it is true that Stalin brutally and systematically targeted his own citizenry (one can argue over the purpose, but that's a different topic), this didn't actually play much of a role in defending against the Nazis (except in one brief sense, but we'll get to that later). As you point out, the Nazis detested the Slavs, but the average Russian citizen really didn't know that in an academic sense. Instead, the average Russian just had to witness the Nazis systematically destroy entire villages and settlements. Remember, the Nazis viewed Russia as lebensraum which meant that Russians had to be removed. Thus, while the Russians may not have understood why the Nazis were exterminating them they very much did know it was happening. While Stalin was brutal the Russians still viewed him as their leader and between their own brutal leader and a foreign people bent on their destruction, the Russians chose their own. Now this opens up a whole other can of worms in the sense of why not just let the Nazis push aside Stalin. There is both an older historical reason and a more immediate. The older historical reason lies in a Russian state of mind particular to the old serfs. Russian serfs believed in a concept known as the "little father" when discussing the Tsar. The concept lays in the fact that the serfs rarely blamed the Tsar for their horrendous conditions. Instead the serfs blamed their masters and viewed the Tsar as their savior. He was the "father" who would protect them and give them land one day. This delusion seved the Tsar wonderfully until Nicholas II's era. Thus, when Stalin emerges it would not be entirely unbelievable to assume some of the old "little father" idea could very well have survived. Now the more immediate reason why the Russians didn't turn on Stalin was the work that the Soviets had done to create a cult of personality around Stalin. Stalin was brutal but only to those deemed "enemies of the state/revolution." For the average citizen, this meant that Stalin was defending the revolution and Russia. Those killed were evil counter-revolutionaries. The more educated within Russia would know what was actually happening but the average citizen may not have. This consequently created a cult around Stalin. Stalin was a savior and the country must defend him and themselves. The Soviet bureaucracy also reinforced this idea through propaganda. So, between the cult of personality and the "little father" concept, the average Russian may very well have viewed Stalin as their defender rather than their persecutor. Just as a final note there were other reasons for the Russian allegiance to Stalin in WWII. One is simply if you ran or retreated there were orders to shoot you. This order is most likely over-exaggerated but it did exist. Another reason for loyalty to Stalin was Stalin's ability to call upon Russian nationalism during the war. Rather than rely on communist ideology, Stalin cleverly used Russian nationalism. He consistently used old Russian concepts like Orthodoxy and the "Motherland" to rally the forces. Thus, Russians felt more like they were fighting for Russia rather than for Stalin or the nebulous idea of communism. Put all together, these reasons worked to Stalin's advantage. The Nazis were intent upon Russia's destruction, the average Russian may not have entirely viewed Stalin negatively, and Soviet progranda evolved in such a way as to shield Stalin.

As for sources (I'm on mobile so I do apologize for any formatting issues) Anthony Beevor's book Stalingrad is a good look at a pivotal battle as is Andrew Nagorski's The Greatest Battle which looks at the Battle of Moscow. For more broad analyses of Stalin, Everyday Stalinism by Sheila Fitzpatrick offers a good look at life under Stalin and Robert Service's Stalin is a good biography.