Although Kant was the first to refer to the distinction as such, his belief that there is a form of truth based on predicates-contained-in-subjects actually goes back at least to one definition from Aquinas of a form of self-evident truth. (Please just trust me on that: otherwise I'll have to go scour the Summa Theologica for the exact citation, a task I haven't had enough coffee for this morning.) Down the road, Quine counterargued (implicitly) that either meanings don't specifically ground a certain class of truths, or they ground all of them, but in such a way that analytic apriority is ruled out. My understanding of Quine's judgment is that we can take a supposedly analytic statement like, "Bachelors are unmarried men," and rephrase it as what would supposedly be a distinctly synthetic one, "The word 'bachelors' refers to unmarried men." This latter would be synthetic as the fact that a specific word refers to a specific set of things is not analytically true; one cannot just a priori analyze the word-type (the type of the string of letters) to determine what the word-tokens are correlated with.
Of course, by stipulative definition we can a priori restrict our reference class when using a certain word, but even a proposition like, "I henceforth stipulate to always use 'bachelors' to refer to unmarried men," is synthetic, as the subject "I" would be synthetically related to the predicate "henceforth stipulate that..." So at best, "things true by virtue of the meanings of their words" wouldn't be analytic but synthetic, and still contingent, so not otherwise a priori as with Kant's characterization of apriority as involving necessity. (Or: even the synthetic a priori can be immediately contingent, which would undercut the rationalism of the Kantian model, adverting to Quinean empiricism.)
So far so good. Now on the other hand, let us try to interpret the analytic/synthetic distinction not in terms of the truth of propositions in general, but in relation to propositions as answers to questions. Rather than say, "An analytic truth is one where the subject logically contains the predicate,"* we would say (we'll start with a slightly circular description), "An answer to a question is known analytically if that answer is known by analysis of the question." For example, take, "What are bachelors?" Thinking of the wh-term as a variable, we then "solve for" the variable by analyzing the meaning of "bachelors" ("bachelors" being the only thing at hand with a semantic value that can solve for the variable). Then, "Bachelors are unmarried men," is known to be true by analysis not "because the predicate is contained in the subject" but for a subtly different reason.
By contrast, synthetic answers would then require information from outside the question, to "solve for" the variables. For example, thinking about Sarah in general will not answer our question, "Where is Sarah?" (or, the only analytic knowledge here is of the answer, "Well, she's somewhere," which however might be false if Sarah has ceased to exist: so maybe not even that, but only, "Well, she's either somewhere or nowhere," which is of course basically useless). For that, we need external information about Sarah's location, a perception of her in external space.
Again, so far so good. But then are only wh-term questions relevant to the analytic/synthetic distinction thus conceived? How would we apply the distinction to a yes-no question like, "Is Sarah in South Africa?" But so here, by a tortuous definition, we might say, "Yes, Sarah is in South Africa," is synthetically known to be true because there is a wh-term counterpart question, "Where is Sarah?" whose answer, "Sarah is in South Africa," is synthetically known (if known in the first place). The synthetic truth of a yes-no answer is a complex relation between the form of a yes-no question and a wh-term question, then.
The Quinean reply would then be that e.g. "What are bachelors?" can be rephrased, "What does the word 'bachelors' refer to?" So think of the erotetic distinction in functional terms. Let us have a function f(x) = x+y, say. The presence of variables makes the function "erotetic" after a fashion. Then we say that f(x) = 4 (or 5 or 6 or 7 or some other particular, determinate value) when we input information external to the form of the function, e.g. if we put in 2 for x and y; and, "f(x) = 4," is known to be true, if it is, by this synthesis. But f(x) = (x+y)+y is a "true equation" here that results from simply taking the function by itself for its own input. So equations of the function involving completely specified values are known to be true equations by synthesis of possible external inputs and functions, whereas equations of the function that just take the function for the input are known to be true by analysis.
To be sure, analytic knowledge thus obtained is so easily had as to make its possessors not that much better off, epistemically, than they were before they had it. It is by and large "trivial." Kant himself didn't deny this, though (and if you note his discussion of "the meaning of the word 'water'" in the first Critique, you'll find that he very well anticipated Kripke's remarks about the apparent analytic aposteriority of, "Water is H2O"). The question, "What is the point of conceptual analysis?" doesn't have a very good answer in relation to individual concepts, though. Analyzing the concept of knowledge by itself, dealing with Gettier cases, and so on, doesn't really get us anywhere; the point is to see if, by analysis, we ever end up with basic, unanalyzable concepts (now, if the concept of knowledge is sui generis). The value of conceptual analysis is not in the answers it gives us to questions about individual concepts but in what it shows us about systems of these.
So: Is the above-described difference between types of ways to answer questions a substantive enough difference to ground a significant epistemic distinction? Or does it just collapse under Quinean pressure, like other definitions of the analytic/synthetic distinction?
*[Addendum: there are hypothetical questions, too, like, "If X, then what?" I think that consequents can be thought of along the lines of predicates of antecedents, i.e. the subject-predicate relation between terms in a categorical proposition is kindred to the antecedent-consequent relation between propositions in a hypothetical. But I vaguely remember objections to the relative poverty of Aristotelian logic on just such a ground, as (part of) what led to Frege's function-argument vs. subject-predicate representational scheme for propositions in general, so I don't want to press the analogy too hard here.]