Arsenal went into the game needing to win to secure Champions League football next season, but having never won a Uefa competition match against another English club in six attempts.
The Gunners had also lost four of their five previous European finals, although boss Unai Emery won the Europa League on three occasions when in charge of Spanish side Sevilla.
However, it wasn’t to be for Emery in the Azerbaijan capital as the Blues struck first blood early in the second half when former Arsenal striker, Olivier Giroud, grabbed his 11th Europa League goal of the season to move out on his own at the top of the tournament’s scoring charts.
Pedro added a second on the hour, before Hazard looked to have made the game safe at 3-0 with a penalty five minutes later.
But Alex Iwobi pulled one back for the Gunners to give them a glimmer of hope only for Hazard to snuff it out moments later with his second of the game in what is likely to be his final Blues’ appearance.
It secured Chelsea their second Europa League title in six years, while handing boss Maurizio Sarri his first major piece of silverware.
Chelsea were boosted by having N'Golo Kante passed fit even though he trained separately on Tuesday because of a knee injury, while Giroud got the nod over Gonzalo Higuain to start up front.
Arsenal had former Chelsea man Petr Cech in goal for the final game of his career, while both strikers, Pierre-Emerick Aubameyang and Alexandre Lacazette, started with Mesut Ozil behind them.
Ozil had the first chance of the game on eight minutes, but the German fired wide after a nervous clearing punch from Blues’ keeper Kepa Arrizabalaga fell to him on the edge of the area.
Arsenal then had a penalty appeal in the 18th minute when Lacazette went down in the area after Kepa dived at his feet to prevent him getting a shot of goal.
There looked to be barely any contact between the duo and, after the referee Gianluca Rocchi briefly checked with the Video assistant Referee (VAR) play was allowed to continue.
Arsenal continued to look the more likely to open the scoring and went close on 28 minutes when Granit Xhaka hit a rocket of a shot from outside the area which clipped the top of the Chelsea crossbar.
Chelsea responded and, after Hazard managed to draw in a couple of Gunners’ defenders, he laid the ball to Emerson on the left of the area, but his strike was well blocked by Sokratis.
The Blues continued to claw their way into the game and they went close again on 34 minutes when Emerson did manage to get a shot at goal, but this time Cech was on hand to parry the ball away to safety.
On 40 minutes Cech pulled off an even better save to deny his former club when he got down to his left to push away a Giroud strike from the edge of the area which was heading towards the bottom corner of the net.
After a disappointing first half, the second half came to life just four minutes in when Emerson whipped a lovely ball into the area from the left and Giroud got ahead of Laurent Koscielny before guiding the ball just inside the post with a superb diving header.
It was 2-0 on the hour when Mateo Kovacic played the ball to Hazard on the left side of the box and he teed up Pedro who clinically guided a left-foot strike beyond the dive of Cech from the middle of the area.
Chelsea were then awarded a penalty minute when Giroud was barged over inside the area by Ainsley Maitland-Niles and Hazard stepped up to convert from the spot past Cech on 65 minutes.
Arsenal got a foothold in the game four minutes later when Iwobi struck a superb half-volley from just outside the area which flew into Kepa’s far corner of the net.
But any hopes of a comeback evaporated on 72 minutes when Giroud collected a pass from Hazard down the left of the area and then picked out the Belgian to convert his second of the night from close range.
Chelsea could have heaped more misery on Arsenal as Cech produced an exceptional save to deny Willian, before Cesar Azpilicueta fired just wide of the far post from the right of the area on 81 minutes.
Arsenal did have opportunities to reduce the arrears in the closing stages as Kepa did well to deny Lacazette, before Andreas Christensen produced a good block to prevent Aubameyang from putting the rebound into the net from close range.
On 84 minutes, youngster Joe Willock exchanged passes with Lacazette but curled his effort past the advancing Kepa and wide of the far corner.