Khouki met Akram Afif's free kick four minutes into the second half to put hosts Qatar ahead, and the Asian Player of the Year unlocked the UAE defence again with 16 minutes left, delivering the free kick from which Miguel headed in.
Qatar's Tarek Salman was sent off in the 89th minute, and Sultan Adil pulled one back for the UAE nine minutes later in a nail-biting finish that featured more than 15 minutes of stoppage time.
The win means the Qataris top Group A with four points ahead of the UAE on three and Oman with one in the fourth round of the Asian qualifying competition.
Qatar will be appearing at a second consecutive World Cup finals after making their debut at the finals as hosts in 2022.
The UAE continue on to a two-legged clash next month against either Saudi Arabia or Iraq, with the winner of that game progressing to the intercontinental playoff in March.
Julen Lopetegui's Qatar side needed to win to qualify, and UAE goalkeeper Khalid Eisa was called upon to deny Sultan Al-Brake in the early exchanges, while Nicolas Giminez flashed an attempt wide at the other end in a tense opening.
Lucas Pimenta should have put the visitors in front on the quarter-hour mark, having peeled away from his marker to meet Ali Saleh's cross, only to head narrowly wide of Qatar goalkeeper Mahmud Abunada's right post.
Qatar's Edmilson Junior was millimetres away from connecting with Afif's inswinging cross from the left, and Mohammad Manai nodded his attempt wide as the home side increased the pressure.
The Qataris went in front just after the break, Saleh's foul on Edmilson Junior setting up Afif to deliver a curling free kick from the right that Khouki gleefully headed home.
Afif unlocked the UAE defence again in the 74th, floating in a free kick from the other flank that sailed over Eisa's head, and Pedro headed in from close range.
Qatar's Salman was sent off for a reckless lunge on UAE substitute Erik, and Adil buried his low shot into the corner to set up a dramatic finish, but Lopetegui's team held on.
