UAE was on course to advance inside 90 minutes when Ali Ahmed Mabkhout netted for the third game in a row to give his side a 2-1 lead after Khamis Esmaeel's opener was cancelled out by Mirlan Murzaev's header.
However, substitute Tursunali Rustamov forced extra time with a near-post header in second-half stoppage time, only for UAE to go ahead for a third time through Khalil's decisive 103rd-minute spot-kick.
UAE now has a chance to avenge its 2015 Asian Cup semi-final loss to Australia in the 2019 quarter-finals, with the Socceroos winning 2-0 four years ago en route to claiming the tile on home soil.
Alberto Zaccheroni's side struck first from a corner routine that saw Ismaeil Matar's delivery nodded on by Khalifa M Ghanim and then flicked in by Esmaeel's head.
Yet Kyrgyzstan responded 12 minutes later, Murzaev taking the ball around goalkeeper Khalid Eisa Bilal and squeezing home despite the presence of two defenders trying to clear off the line.
Nineteen minutes into the second half Mabkhout, who was top scorer at the 2015 Asian Cup, capitalised on some slack defending to stay onside and make it 2-1.
Kyrgyzstan, for whom Tamirlan Kozubaev squandered two great chances from close range, were heading out until substitute Rustamov headed in Anton Zemlianukhin's near-post corner in the 91st minute.
It was UAE which came up with an extra-time winner when it was awarded a soft penalty after Mabkhout hit the deck when held by Bekzhan Sagynbaev, and Khalil rolled his penalty down the middle and in off Kutman Kadyrbekov's trailing leg.
Kyrgyzstan was unable to respond for a third time, with Bakhtiyar Duyshobekov and then Rustamov, the latter in the final seconds, denied by the woodwork.