Both sides traded sets in an entertaining encounter, before the hosts got over the line with a 15-6 win in the final set.
"We are really very tired, both physically and morally. We are on our feet the whole day and I really want to sleep," Azerbaijan captain Odina Bayramova told reporters.
"We spent a lot of our energy in the game with Poland [on Wednesday], however these excuses are unacceptable. We should have won much earlier in this game."