What type of equipment can I use to record a live rock performance as a member of the audience?
You can use portable recorder like Zoom H4n or similar. Recorders like this usually have XLR input that could be plugged directly to mixer. You'd then set input type on your recorder to line-in and set its sensitivity to have your levels not too quiet but not clipping (exceeding the scale).
You can also plug in microphone and try to do the same however investment into microphone + recorder seems pretty high considering the fact, that your recording might be better, but still very much sub par.

Higher quality recorders might have a jack for headphones so you could monitor audio quality of your recording or even line-out you could plug into your DSLR audio-in for easier audio-video sync in post.

Apart from Zoom recorders, another popular brand is Tascam. If you don't want to buy, they can be usually rented in rentals for videographers and filmmakers.