The relationship between reason and morality is most extensively and famously addressed in Kant's "Critique of Practical Reason." In this context, "practical" refers to judgments of morality or the determination of proper actions.
To understand the connection really brings in the whole Kantian system, on which I'm no expert, but let me try a sketch. First, Kant distinguishes between instrumental or "hypothetical" reason and reason per se. His hypothetical reason, what you call contextual, is reasoning from any given end. If you want X do Y. This would even include utilitarian or consequentialist moral thinking, if you want the greatest good for the greatest number...do Z.
But Kant is, like you, a universalist who believes that there are absolute moral duties no matter what the consequences. He bases this not on divine injunction or dogma, but on the internal coherence of reason itself. He argues that we have certain a priori categories of reason that are evident in all experience, for example, the categories of space and time.
We also have freedom of will or self-determination, so we are not bound by the causal necessities of the sensible or "phenomenal" world. We can form judgments about what ought to be and what we ought to do, which can be given in experience. Kant likens this to a different form of "causality" found only in the will of self-conscious rational beings.
He then argues that true, unconditional moral imperatives, or "categorical" imperatives, conform with reason itself. These are maxims, like the golden rule, that we can will to be universally binding without internal contradiction. An example is the way in which lying is ultimately contradictory. If everyone universally lied, then lying itself would not be possible.
So, for a utilitarian we might morally lie to save a life, for example. For Kant, not so. It is a categorical imperative of reason, not unlike an axiom of geometry. And, Kant adds, the consequentialist makes the false assumption that she can ultimately predict the consequences, for example, of the "good lie," which we simply cannot know in the realm of free actions. In any case, to get the better of your friends without resorting to dogma, you want to brush up on a bit of Kant.