Having hit the post early on, Miroslav Klose was on hand to break the deadlock just after the half-hour mark on Wednesday during a commanding first-half performance from Stefano Pioli's men.
But the defending champions - who beat Fiorentina in last year's showpiece - battled back courtesy of Gabbiadini's tap-in, following some great work from Gonzalo Higuain.
The result will likely be seen as a missed opportunity for Lazio, who will now most likely need to record a first win in six years at Stadio San Paolo to make the final.
Lazio came into the game on a run of three straight wins in all competitions and enjoyed a bright start.
Klose could have opened the scoring after nine minutes, but his header into the ground from a pin-point corner was denied by the post.
The German then forced a smart save from Mariano Andujar with another header two minutes later, before Marco Parolo blazed a speculative half-volley over the crossbar from distance.
A much-changed Napoli side struggled to match tempo of their hosts, although home goalkeeper Etrit Berisha was called into action after 20 minutes to gather Higuain's tame drive.
Higuain, the last-gasp match-winner in Napoli's quarter-final triumph over Inter, should have provided a sterner test for Berisha eight minutes later, breaking free of his man to meet Dries Mertens' ball into the six-yard box, but he could only poke his effort straight at the goalkeeper.
Lazio continued to look the better side, and they were rewarded for their efforts 12 minutes before the break with a fine counter-attacking move.
A defence-splitting pass from Felipe Anderson was enough to pick out Klose, who raced into the box before applying a clinical finish.
Higuain fired wide for the visitors two minutes before the break, before Miguel Britos was on hand to clear Anderson's effort off the line at the other end.
The visitors stepped up their efforts after the restart, with Berisha nearly undone by Gabbiadini's deflected free-kick after 53 minutes, but he did well to produce an inspired reflex save.
That chance clearly invigorated the visitors, and five minutes later they were level.
A pin-point ball from Jonathan de Guzman allowed Higuain to get in behind his marker, before he rounded the goalkeeper to tee-up Gabbiadini, who was left with a simple tap-in from close range.
Klose saw a vicious 25-yard drive tipped over at the other end after 62 minutes, before a crucial touch from Stefan de Vrij denied substitute Balde Keita 15 minutes from time.
Mauricio headed wide late on as Lazio searched for a winner, but Napoli held on for a hard-earned draw that leaves the tie finely poised.
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