Implementing AES-CBC (Matasano Crypto Challenge 10)
I suppose you have removed the base64 decoding, so you are working on the raw data.

Then indeed the first block is decrypted as if we were in ECB-mode, because after decrypting the first block, we xor with the IV, which is all 0 and indeed has no effect. 

However, the IV for the next block will be the original previous ciphertext block. So after decrypting that block we have to xor with this new IV, so there we cannot suffice with just ECB mode. See also this picture from the comments: