Zombies come from horrific science experiments gone array, which mutate our self awareness to blood thirsty, flesh eating drones of rampaging killing machines. They don't sleep, they don't breed, they don't think, they just kill and eat, kill and eat. Without having any strategies for battle or any concept of leadership, simply put they can only kill what's right in front of them if that thing has no ability to defend itself. They don't have the brainpower to use weapons, and they certainly don't know how to ambush a prey. With that being said they can however attack by hordes and devour entire cities in days. Leaving behind a mess of rotting corpse, who will soon add to the multitudes of zombies aimlessly seeking out their next meal.
Unicorns have the upper hand in battle against these zombie drones, they can fly to safety, swoop in and attack from higher ground, using their horns to gorge the heads of the undead. Killing them on spot. The other advantage is they can communicate through their horse like language, planning out flanking movements, traps, and when to attack. Sending in hundreds of flying horned unicorns at once to destroy entire groups of zombies. With magic powers galore the fleet of unicorns could very well eliminate the zombie population rather quickly. The only downside to this is they would need to be careful not to allow any of their unicorn brethren to be bitten by the zombies, for this would add to the zombie's ability to seek out the unicorn's lair. If only one unicorn was to become one of the undead, it would carry with it the standard unicorn powers of flight, thus enabling it to bring the battle to new heights, the air. And I'm afraid that if this were to happen, it would be difficult for the other unicorns to attack it being they actually have hearts of pure gold, and might not have the testicular fortitude to kill one of their own?
I'm skeptical to think that the unicorns wouldn't eventually understand that they would have to end the life of a fellow horned magical comrade. Remember they can actually think for themselves and communicate quite well. The ability to escape on wings of awesomeness would improve their battle tactics plus allow them the advantage of air strikes, but it might only take one zombie unicorn to defeat the godly creatures.