Webster's Dictionary of Synonyms (1942) offers a detailed and thoughtful discussion of the two words as they were then used. The first interesting thing about the dictionary's handling of the two words is that it divides its coverage of justify into three discrete parts.
One part consists of an attempt to distinguish between justify and warrant:
Justify, warrant are here compared as meaning to afford as evidence, a circumstance, a situation, a state of affairs, or the like, good grounds for doing, saying, using, or believing something. Justify implies the provision of grounds so good that they satisfy one's reason and, often, one's conscience, especially if there is a conflict between what seems necessary and what is morally right; as "He says that more men are killed by overwork than the importance of this world justifies" (Kipling); "no consideration on earth justifies a parent in telling lies to his child" (B. Russell). "I remember a very tender-hearted judge being of opinion that closing a hatch to stop a fire and the destruction of a cargo was justified even if it was known that doing so would stifle a man below" (Justice Holmes). ...
A second part considers the meaning of justify in contradistinction to maintain, assert, defend, and vindicate:
Maintain, assert, defend, vindicate, justify come into comparison when they mean to uphold as true, right, just, valid, or worthy of notice or acceptance in the face of opposition or indifference. ... Justify (as here compared) implies that the thing concerned can no longer be opposed or ignored, because it has conclusively been shown to be true, valid, proper, or the like, by irrefutable arguments, or on inescapable grounds, such as its consequence, its successful operation, or the like. "If the Germans are to justify the high claims they make for Lessing as a critic, they must rest them on other grounds than his intellectual originality" (Babbitt). "Fate persists in justifying the harsh generalizations of Puritan morals" (Bennett). "It isn't by the materials you use that your claim to originality will stand justified or condemned; it is solely by the thing you do with them" (Lowes).
And a third part (which most closely concerns the poster's question) addresses justify as a synonym of explain, account for, and rationalize:
Explain, account for, justify, rationalize are synonyms when they mean to give or tell the cause, reason, nature, or significance of something obscure or questionable. ... One justifies oneself or another when one explains certain acts or behavior in an attempt to free oneself or another from blame. It may or may not imply consciousness of guilt or a definite accusation. "Powell...began to justify himself. 'I couldn't stop him,' he whispered shakily. 'He was too quick for me.'" (Conrad). "So far is he from feeling the pangs of conscience that he constantly justifies his act" (G. L. Dickinson). "In her heart she did not at all justify or excuse Cyril" (Bennett). One rationalizes that which is or seems to be contrary to reason when one attempts an explanation that is in accord with scientific principles or with reality as known to the senses; as, to rationalize the Greek myths; to rationalize the Genesis story of creation. In very modern use, rationalize often comes very close to justify without, however, so strong an implication of blame and with the added implication of self-deception and, at times, of hypocrisy "In other countries the plutocracy has often produced men of reflective and analytic habit, eager to rationalize its instincts" (Mencken). "Propaganda...is influential only when it is a rationalization of the...prejudices or interests of those to whom it is addressed" (A. Huxley).
The most striking thing about this last excerpt is its suggestion that rationalize had only recently (as of 1942) begun to be used in a way that created a strong overlap with justify. Still, Webster's takes the view that one more frequently justifies in response to criticism or blame, while one more often rationalizes when one is deluded or hypocritical.
A further development in the sense of rationalize appears in S.I. Hayakawa, Choose the Right Word (1968) in a discussion of the noun form rationalization in comparison with lie, falsehood, fib, prevarication, and untruth:
These words refer to statements or formulations that are misleading or contrary to fact. ... By contrast, rationalization is very specific, indicating a thought process by which one attempts to justify one's actions, either to oneself or to others, by consciously or unconsciously distorting the truth. Although psychologists may view all formulated explanations as rationalizations, the word has become a fad word for ingenious but specious reasoning that puts one's own behavior in the most favorable light possible: The psychiatrist works to get behind the web of rationalizations to the real conflicts and anxieties they conceal; his rationalization that being late for work was a forgivable foible, considering how indispensable he was to the office; Nazis whose rationalization was that they were only following orders.
It appears that use of justify in the sense of "attempt to excuse from blame or to render respectable" has been around for a long time. The implication that it comes in response to criticism or disapproval is very strong, as the Webster's discussion points out; but as a means of making an excuse, it need not rely on an elaborate or rigorous logic.
In contrast, rationalize is a relative latecomer to the scene and had as its original meaning "attempt to reconcile a nonrational claim with reason or scientific knowledge." In its self-serving sense, rationalize puts considerable store in the presentation of a reasoned (or superficially reasoned) argument in favor of a deed or course of action. Because the persuasiveness of the argument is central to the effort to rationalize, a person offering this type of assertion may be more susceptible to self-delusion or (on the other hand) more guilty of a cynical disregard for truth.
Consistent with these distinctions, asserting that "might makes right" may justify exploitative treatment of the weak by the strong, but it does not rationalize such treatment.