First, Darwinian science supports classical liberalism's devotion to the British Enlightenment tradition of thought as opposed to the French Enlightenment tradition. Although I don't explicitly make this point in my Cato Unbound essays, I elaborate this point in Darwinian Conservatism.
In The Constitution of Liberty (1960), Friedrich Hayek distinguished between two traditions of liberty associated with England and France.
we have had to the present day two different traditions in the theory of liberty: one empirical and unsystematic, the other speculative and rationalistic--the first based on an interpretation of traditions and institutions which had spontaneously grown up and were but imperfectly understood, the second aiming at the construction of a utopia, which has often been tried but never successfully. Nevertheless, it has been the rationalist, plausible, and apparently logical argument of the French tradition, with its flattering assumptions about the unlimited powers of human reason, that has progressively gained influence, while the less articulate and less explicit tradition of English freedom has been on the decline. (54-55)
Later, Thomas Sowell's A Conflict of Visions (2002) showed how much of the ideological debate over the past two hundred years could be understood as a debate between the "constrained vision" of the British tradition and the "unconstrained vision" of the French Tradition. Then, Gertrude Himmelfarb's The Roads to Modernity: The British, French, and American Englightenments (2004) sketched the history of these competing Enlightenment visions.
I have argued that Darwinian science is on the side of the realist vision of the British tradition of liberty. The central idea of this realist vision is evolution--the idea that social order is largely spontaneously evolved rather than rationally designed. Darwin's theory of biological and cultural evolution grew out of the social theory of evolved, spontaneous order that was developed by Adam Smith and others in the Scottish and British Enlightenments. Steven Pinker, in The Blank Slate (2002), showed how modern biological research on human nature confirms the insight of the realist vision that there is a universal human nature--imperfect in knowledge and virtue--that cannot be radically changed by social reform. Most recently, David Brooks's The Social Animal (2011) argues that recent research in cognitive science supports the British tradition against the French Tradition.
The second way in which Darwinian science supports classical liberalism is in supporting the liberal distinction between society and state. Darwin's evolutionary explanation of the moral sense shows how moral order can arise through the natural and voluntary associations of civil society without the need for coercive governmental enforcement by the state. This sustains the classical liberal distinction between the political order of the state as protecting individual liberty and the moral order of society as shaping virtuous character. Consequently, a Darwinian liberalism can combine an Aristotelian ethics of social virtue and a Lockean politics of individual liberty.
Regrettably, many thinkers in the Aristotelian tradition of political thought--particularly, Leo Strauss and his followers--fail to recognize this distinction between society and the state, because they don't see the ambiguity in the ancient Greek conception of the polis as signifying both a society and a state. Here is where I agree with Douglas Rasmussen--in a recent essay for Cato Unbound--who criticizes the Straussians for ignoring this distinction and for refusing to consider how this distinction supports a union of Aristotelian virtue and Lockean liberty.
The third way in which Darwinian science supports classical liberalism is in showing how moral order can be grounded on purely human sources of order--human nature, human culture, and human judgment--without any necessity for appealing to supernatural or cosmic sources. This is important for classical liberalism because if the liberal principle of equal liberty for human beings depends upon some religious conception of human beings as divinely created, then it would seem that a liberal regime would have to enforce some theocratic conception of moral order as grounded in religious belief, which would deny the liberty of thought that is crucial for liberal thought.
The fourth way in which Darwinian science supports classical liberalism is in confirming the liberal history of government as set forth in the political anthropology of Locke, Hume, and Smith. An evolutionary history of government manifests three eras in political history: the Paleolithic era of egalitarian hierarchy in foraging societies, the pre-modern era of despotic hierarchy in agrarian states, and the modern era of egalitarian hierarchy in commercial liberal republics.
In this history, we see the difficulty in combining freedom and civilization. Foraging societies were free but uncivilized. Agrarian states were civilized but unfree. Commercial liberal republics are both free and civilized.
We can judge this history to be progressive insofar as it's a cultural history of trial and error in trying out various ways of organizing society and politics, as a result of which we eventually see the emergence of modern liberal regimes as successful because they happen to satisfy the full range of natural human desires more adequately than any prior regimes.
Some previous posts on related themes can be found here, here, and here.