Mouctar Diakhaby headed Valencia into an early lead at Emirates Stadium on Thursday but within 14 minutes the Gunners had turned the tie around.
Lacazette first finished off a swift counter-attack involving Mesut Ozil and Pierre-Emerick Aubameyang before heading home Granit Xhaka's cross to put Unai Emery's men in front.
And the Spaniard, a three-time winner of the competition with Sevilla, will take a two-goal lead back to former club Valencia for next week's second leg after Aubameyang struck late on.
Arsenal trailed in the 11th minute, having already failed to heed a warning from a Dani Parejo set piece that was eventually turned over the crossbar by Ezequiel Garay.
His defensive colleague Diakhaby would not make the same mistake, nodding in at the back post when Rodrigo Moreno headed Parejo's corner back across goal, but Valencia's advantage did not last long.
Ozil and Lacazette combined well to send Aubameyang through with the Gabon international superbly teeing up his strike partner to tuck home.
And Arsenal took the lead in the 25th minute, with Lacazette's downward header from a fine left-wing Xhaka cross parried into his own goal by Neto, via the post.
Parejo's free-kick flew over the crossbar while Lacazette somehow missed a golden chance to seal his hat-trick by failing to connect with Aubameyang's centre.
Lacazette wasted an even clearer opportunity in the 68th minute, firing straight at Neto from close-range and again failing to beat the goalkeeper on the rebound.
Petr Cech denied Kevin Gameiro and the striker volleyed over as Valencia launched a late rally.
It was Arsenal who struck a potentially decisive blow, though. Neto kept out Lacazette brilliantly but was unable to stop Aubameyang from turning home Sead Kolasinac's deep cross.
What does it mean? Emery weaving more Europa League magic
Arsenal had lost three Premier League games in a row since winning 1-0 away to Napoli in the last round, but they showed strong character to bounce back after a sloppy start to the first leg.
Emery, whose Sevilla side knocked Valencia out at this stage of the Europa League in 2013-14, will now fancy his side's chances of booking a spot in next month's final in Baku, although Marcelino's men have an away goal to comfort them.
Lacazette at the double
For the third year in a row Lacazette scored in the Europa League semi-finals, but in each of the past two seasons his team have failed to reach the showpiece.
The France forward has hit 18 goals in all competitions this term and if Arsenal are to lift the trophy he looks to be their key man, although he should undoubtedly have claimed the match ball.
Neto error key
Lacazette's header to give Arsenal the lead had plenty of power, but Neto will surely feel he ought to have kept the effort out. He somewhat made amends with a fine double save from the Arsenal striker, though.
Key Opta Facts:
- Arsenal have progressed from 37 of their 40 ties in all European competitions when winning the first leg, though Valencia were one of the three teams to eliminate them, in the 2000-01 Champions League quarter-final.
- This is the 28th time Valencia have lost the first of a two-legged European tie – they have ended up winning the tie on 11 previous occasions, most recently against Basel in the 2013-14 Europa League.
- Mouctar Diakhaby's opener for Valencia was the first home goal Arsenal had conceded in the Europa League since the group stages, ending a run of 460 minutes without conceding for the Gunners at the Emirates.
- Alexandre Lacazette became only the third player to score a brace in a European semi-final match for Arsenal, after Charlie George in the 1969-70 Fairs Cup and Steve Bould in the 1994-95 Cup Winners Cup.
Arsenal return to the Emirates on Sunday for the visit of Brighton and Hove Albion in the penultimate Premier League game of the season. On the same day, Valencia continue their own chase for Champions League qualification via the league with a trip to LaLiga's bottom side Huesca.