Did the Tannaim and Amoraim believe in magic?

From the Gemara in Sanhedrin (67-68), just covered by Daf Yomi the answer seems clearly yes. The Gemara brings the following stories:

1. (R. Yochanan) Witchcraft is called Keshafim, an acronym for MaCHchiSHim FaMalya (Shel Ma'alah, it contradicts (nullifies decrees of) the Heavenly Court, e.g. that a certain person should live).
2. (Rav Ashi): I saw Karna's father (a warlock) blow his nose. Silk came out.
3. Ze'iri went to Alexandria of Mitzrayim. He bought (what he thought was) a donkey. When he gave it to drink, the Magic ceased, and it reverted to a piece of wood. He requested a refund. The sellers: We will refund your money (due to your stature). We would not do so for others. In this city, a buyer should know to test the merchandise with water, lest it is made through Magic.
4. Yanai (a a Warlock) went to an inn. He asked for water, and they gave  him water with flour. He saw that the lips of the woman who served him were moving. (He suspected that she was doing Magic.) He spilled some on the floor, and it became scorpions. Yanai: Likewise, I will give to you to drink! She drank, and turned into a donkey. He rode on her in the market, until one of her friends saw this and negated his Magic, and she reverted to a woman.

The Gemara clearly takes these stories literally, the proof being the following passage in the same Gemara:

(R. Chanina ): "Ein Od Milvado (there is nothing other than Hash-m)" - even witchcraft (has no power). A woman was trying to weigh the dirt under R. Chanina's feet (for the sake of Magic). He was not concerned. Question: R. Yochanan taught that it [Magic] contradicts the Heavenly Court! Answer: R. Chanina was different. Because his merit was so great, it could not affect him.

We see clearly that the Gemara took the idea of magic working literally and therefore asked how come R' Chanina  was not concerned.

The Rambam claims (in all his major works) that magic doesn't work. He writes (Avoda Zara 11:16):

ודברים האלו--כולן, דברי שקר וכזב הן; והן שהטעו בהן עובדי עבודה זרה הקדמונים לגויי הארצות, כדי שיינהו אחריהן.  ואין ראוי לישראל, שהן חכמים מחוכמים, להימשך בהבלים אלו, ולא להעלות על הלב שיש בהן תעלה

And these things [magic] are all lies and falsehood and this is what fooled the original one who worshipped false goods so that people would follow them. It is not worthy of Jews who are smart people to believe in these idiocies and to think that they have any effect.

However, the Rambam is pretty much alone on this front as all the other major rishonim disagree and state explictly that magic works. They cite this Gemara (above) as one of the major proofs. Likewise, the Gra (Yoreah Deah 179) says that the Rambam was led astray by accursed philosophy and that these Gemaras about magic need to be taken literally.