Mouctar Diakhaby's early header had given Valencia the lead and a precious away goal but Frenchman Lacazette bagged a double before halftime to settle the jitters at The Emirates.
At 2-1 and with the clock showing 90 minutes the semi-final was precariously-balanced for the return at the Mestalla next week but Aubameyang's late volley means Arsenal will head to Spain as favourites to reach the final in Baku.
Eintracht Frankfurt were held to a 1-1 draw at home to Chelsea in the night's other semi-final, first leg.
Arsenal had lost three consecutive Premier League games to drop to fifth place in the domestic table with two games to go -- seriously undermining their hopes of qualifying for the Champions League via a top-four finish.
But manager Unai Emery has a special relationship with the Europa League having won it three times in a row with Sevilla and delivering the trophy to Arsenal for the first time now looks their most likely route back into the elite tournament.
"We know it's going to be hard (in Valencia) so of course getting as many goals as we could is better for us," Lacazette, who should have been celebrating a hat-trick, said.
"Thankfully Auba scored the third one.
"We want to win the Europa League to go straight to the Champions League but also to win a trophy."
DREADFUL OPENING
Arsenal had conceded nine goals in their last three Premier League games and it was easy to see why in a dreadful opening.
Valencia, themselves struggling to secure a top-four spot in La Liga, could not believe how easily they sliced through the home defence and had already gone close to scoring before towering Frenchman Diakhaby put them ahead.
When a corner was swung over, an unmarked Rodrigo headed it back across goal where Diakhaby rose above three stationary Arsenal defenders to nod into the net.
For a while there was panic in the Arsenal ranks and both Daniel Parejo and Goncalo Guedes went close to a second goal, but the hosts equalised with a stunning breakaway goal seven minutes after going behind.
Lacazette started the move, releasing Aubameyang with a superb pass. The Gabonese forward surged into the area but instead of shooting, turned back inside and rolled the ball for the on-rushing Frenchman to slide his shot past Neto.
Another seven minutes passed before Arsenal took the lead.
Granit Xhaka's cross found Lacazette and although his header lacked power it bounced off the turf and just went over the line despite Neto's desperate attempt to keep it out.
Suddenly Arsenal were rampant and another Xhaka cross found Aubameyang but he bounced his volley over the bar.
Valencia burst back into life at the start of the second half and it needed a brave header by Arsenal captain Laurent Koscielny to stop a cross reaching the dangerous Goncalo Guedes.
Lacazette wasted two gilt-edged chances to put the hosts in control, first fluffing a header from Aubameyang's cross with the goal gaping then weakly shooting straight at Neto.
Valencia, losing semi-finalists in 2012 and 2014, would have been reasonably content heading back to Spain with a 2-1 defeat but they switched off in the dying seconds.
Moments after Neto had made a superb save, Arsenal kept the ball alive and Sead Kolasinac's superb cross found Aubameyang at the far post to drive his volley home.