Since my excessively heavy dictionary (American Heritage Dictionary, 4th Edition) is already out, I might as well see what it has to say on the subject.
evoke tr.v. evoked, evoking, evokes 1. To summon or call forth: actions that evoked our mistrust. 2. To call to mind by naming, citing, or suggesting: songs that evoke old memories. 3. To create anew, especially by means of the imagination: a novel that evokes the Depression in accurate detail. [Latin evocare, to call.]
Synonyms evoke, educe, elicit These verbs mean to draw forth or bring out something latent, hidden, or unexpected.
So, basically, evoke means to call to mind, to create internally. When an author evokes the wind, they create the feeling or image of the wind in the mind of the person reading the text. You can also evoke things by accident - a beautiful melody can evoke a memory of the time your mother taught you to play the piano, although the musician may not have intended to do so.
provoke tr.v -voked, -voking, -vokes 1. To incite to anger or resentment. 2. To stir to action or feeling. 3. To give rise to; evoke: provoke laughter. 4. To bring about deliberately; induce: provoke a fight. [Middle English provoken, from Old French provoquer, from Latin provocare, to challenge.]
Synonyms provoke, incite, excite, stimulate, arouse, rouse, stir These verbs mean to move a person to action or feeling or to summon something into being so by moving a person. Provoke often merely states the consequences produced: "Let my presumption not provoke thy wrath" (Shakespeare).
Note that in the definition of provoke, the word evoke is cited, but only in one of the four uses. These words are very similar. The main difference between them is the fact that provoke has lots of negative connotations attached to it. You generally won't see people provoking someone to hug other people, but instead to punch them in the face. It's related to the Latin root meaning challenge, which adequately describes the general antagonistic effect desired by the use of the word provoke.
As the other answers mentioned, provoking is generally a very physical thing. It involves words, actions, physical stimuli. Evoking, on the other hand, is generally very related to feelings, thoughts, and memories. It tends to be much more emotional.
Provoke is also distinct in that it requires an external provoker. You can evoke something within your mind all on your own - no external intent is required for the whistling of the wind through the trees to call to mind the time you stood on the moor and watched your house burn down as the howling wind brought the ashes to you.
However, external intent is required to provoke - you need a taunter for cruel words to drive you to punch them in the face. You have to have a provoker, and they have to intend to provoke you. (Alternately, you could just assume they mean to provoke you... the whale in Moby Dick didn't really intend to provoke Captain Ahab, he's just crazy enough to believe that it did. As long as intent is assumed, provoking can happen.)
You do not need an evoker to evoke emotions, and the evoker may not even intend to create emotion within the listener. A singer may desire to stir people to tears, but if an audience member is crying because the melody evokes the last song she sang before she lost her voice in a tragic accident, that is unrelated to the intent of the singer.
(All examples were created on the spot by the author.)