First of all, I'm removing the references to evolution as this has been removed from the OP. The rest of this answer should directly address the relationship between the evolution of the brain, social development and the emergence of morals...
Morals don't evolve (biologically at least); they are more of an emergent property of social development. If humans were essentially solitary animals who came together to mate and then abandoned our young to their fate after birth, our moral development would be severely retarded by modern standards.
So, a part of our moral development as animals comes from social interaction and the need to form a set of basic rules for conduct within the group that promotes the group over the individual. When hunting in a pack, coordinated attacks on larger prey only work if every member of the pack does what they're supposed to do. This forms the basis of concepts like trust, duty, etc.
The ability to work as a coordinated team in any form other than (say) an insect 'hive mind' capacity doesn't come to organisms straight off the bat when they get brains, however. The brain has been constantly evolving over a billion years or more, and there are stages to it that allow certain functions.
The oldest part of the brain is the cerebellum, which (for simplicity) can be described as being a hard-wired electrical system. It deals with autonomic functions like regulating the heart and breathing, etc. as well as controlling instincts like hunger, the need to procreate, etc.
Next came the limbic system, or reptilian brain. This is essentially a chemical system and is the seat of emotions. Why did it evolve? Well, sometimes hard-wired instincts work against you and send you into harms way instead of out of it. Also, sometimes what is good for you is not good for your young and puts the species at risk. Emotions are a simple system that provide some context to any instincts driving you and allow you to override those instincts in key situations, like not going for food if the situation looks like a trap or a good place for an ambush.
Finally, we get to the cerebral cortex, which (again for simplicity) can be described as a soft-wired system and is also known as the mammalian brain. This is where our seat of reason is, allowing us to create our own programming to suit a changing environment and allows us to adapt to it within a single lifespan.
It is this last part of the brain that allows us to ignore our emotions and our instincts if we believe there is a sufficiently compelling reason to do so. The other two parts operate in a purely 'selfish' fashion, based on the idea that our own survival means by extension the survival of our species. The cerebral cortex however allows us to cooperate with others and operate within a social framework even when that may not be the best outcome for ourselves.
In humans, we've evolved a sense of empathy as well, and this is at the heart of our moral framework. In an attempt to use strategy rather than strength to hunt, we've developed the ability to put ourselves in the prey's place and figure out what it would do next. In so doing, we can plan a trap that the animal's neural programming will make it just walk into, meaning that we can hunt far larger creatures than us armed with little more than a brain.
The problem is, that empathy has made us acutely aware of our own innate selfishness and the damage that we cause in hunting. We don't refer to our meat by the animal name, we have other names for it like Beef or Pork. We praise ourselves for our sense of sacrifice to each other and to our children especially without giving any thought as to whether we're going too far in not looking after ourselves. (I'm not saying that this is a bad thing, what I'm saying is that our society has evolved to 'expect' us to sacrifice for our children with no further rational discussion on the topic.)
That we have language and formal constructs of reason only means that we can articulate these concepts far more precisely and call them 'morals', but technically any creature with a cerebral cortex and a social structure is capable of some form of morals, even if they can't articulate them to us.
Emotions and Biological Evolution
To address comments, the evolution of emotions and (later) reason is improbable, but eminently practical at the same time. Yes, there is a high energy cost to evolving new systems on top of the cerebellum, but they do give organisms something that conventional evolution cannot; contextual awareness.
The cerebellum can handle situational awareness (There's food over there) and even self-awareness (not sentience, more like 'I'll go to the food because I'm hungry) but what it can't do is help with contextual awareness (I'll save this food for my chick...) or empathy (because it'll be hungrier than I am). Also, there is the contextual awareness of previous experience to consider (I'm thirsty but I'll go to the next waterhole because two of our herd have been taken by a predator at this one).
What emotions and reason give life is the ability for a single organism to adapt to its changing environment, rather than having to do it the old fashioned biological way involving many generations. This gives a MASSIVE boost to survival odds, but does leave us combating our 'instincts' far more often at the same time. This can have mixed results (which is what I was getting at previously with the hunting analogy) but generally speaking, our survival odds are much greater with emotions and reason than without.
To your point about emotions and evolution; we generally believe that all creatures from reptiles up (this includes mammals and birds) are capable of emotions to some degree, perhaps not complex emotions but emotions nonetheless. Mammals for the most part are capable of some form of reason, but it's only humans that can articulate those emotions and reasoning skills with the precision that implies higher intelligence. The singular advantage that we have is the ability to pass on MUCH more of our knowledge at a cheaper energy cost through language, meaning that each new generation can build upon much more of the work of the past. Emotional creatures pretty much have to learn their lessons from scratch; this is still an advantage over being driven by instinct, but the human mind and language allows for a much richer and faster development as a species through knowledge transfer.
Ultimately though, the development of the Limbic System and Cerebral Cortex change the role of evolution to that of organic evolution, allowing the organism itself to adapt to the context of its environment, and later to adapt its environment to its own needs as we've started to do recently (in the history of the earth at least).
To that end, I believe that emotions DO have their roots in the physical evolutionary process and are essentially a mechanism designed to make organisms more resilient while evolution strives to catch up with the new environmental imperatives.