Maurizio Sarri’s side headed into the tie full of confidence after a magnificent 1-0 win at Serie A leaders Napoli a few days earlier.
But an injury to captain Ciro Immobile left them lacking a cutting edge in attack, and Pedro’s first-half opener was cancelled out by strikes from Vangeglis Pavlidis and Milos Kerkez either side of the break.
The result continues a season-long theme of inconsistency for the Aquile, who dropped into this competition after finishing third in their Europa League group amid struggles to perform on two fronts.
The Dutch side will host Lazio in the second leg next Thursday as they bid to win the comepetition currently held by Lazio’s Eternal City rivals AS Roma.
Lazio’s strong start
It was a bright start from the hosts, who threatened down both wings as Mattia Zaccagni set up Sergej Milinkovic-Savic to steer wide and Manuel Lazzari ran half the length of the pitch before battering a shot well over.
The breakthrough came when Anderson won the ball back in midfield and sent Zaccagni haring down the wing again. The winger picked out Pedro’s clever run and the Spaniard produced the deftest of finishes to find the net.
AZ grew into the game, threatening when a Sven Mijnans volley deflected off Danilo Cataldi and struck the outside of the post, but when they found the leveller it was through a mess of Lazio’s making.
The Biancocelesti tried to pass it out from the back but Milinkovic-Savic was caught in possession and AZ quickly moved the ball forward, Pavlidis dinking a calm finish home from a Jesper Karlsson cut-back.
Enraged by their lapse in concentration, Lazio stormed forward from kick-off and Milinkovic-Savic hammered a 25-yard shot off the bar.
The hosts were back on the front foot early in the second half but lacked sharpness in the final third, with Anderson and Milinkovic-Savic both producing weak finishes from promising positions.
Sarri was left tearing his hair out when the visitors completed their comeback in the 62nd minute by profiting from another turnover in midfield, Kurkaz finishing well to beat Luis Maximiano after Lazio lost the ball and were caught out by a quick transition and clever one-two.
AZ keeper Mathew Ryan almost gifted Lazio an equaliser when he spilled a catch right into Anderson’s path, but the Brazilian’s instinctive finish was off target and he then curled an effort wide of the far post with 10 minutes to go.