In front of a raucous crowd of close to 10,000 at San Mames, the hosts started very brightly, passing well and creating several good opportunities.
They were rewarded for their efforts on 24 minutes with a penalty but it was well saved by Arsenal keeper Reice Charles-Cook to keep the score goalless.
The night got worse for the penalty taker Gulliermo Fernandez as he was shown a straight red card 10 minutes later for a leading elbow which caught Sead Hajrovic.
Arsenal pressed hard to find an opening but the Spaniards were equal to everything that was thrown at them and looked dangerous themselves on the counter-attack. The final whistle ended what was a breathless 90 minutes and keeps Group 6 wide open.
Elsewhere, Olympiacos drew 1-1 with Marseille in the night's other Group Six fixture in Athens.
The visitors looked strong in the opening half an hour, with Omar Diop putting them ahead on 33 minutes with a cool finish.
However, seconds before the break they lost their concentration and a mix-up at the back meant Nikos Ioannidis levelled with an easy finish to take the sides into half-time level.
The second half ebbed and flowed without many clear cut chances, and Marseille lost their discipline towards the end of the game, with two red cards to set up a frantic finish.
The Greeks stormed forward but were unable to take advantage and the game ended in stalemate.