This match started at 11pm local time on Wednesday in Azerbaijan, but it was Thursday by the time it came to life with a flood of second-half goals started by Olivier Giroud's 49th-minute opener against his old club.
Hazard then set up Pedro Rodriguez for Chelsea's second before grabbing a double of his own -- including a penalty -- either side of Alex Iwobi's consolation for Arsenal.
The Belgian is widely expected to leave Chelsea for Real Madrid after seven years in England, and this was the perfect way for him to bow out.
"I think it is a goodbye, but in football you never know," the 28 year-old told BT Sport. "My dream was to play in the Premier League and I have done that for one of the biggest clubs so maybe now it is the time for a new challenge."
English rivals Arsenal, Chelsea all set for Baku face-off
It is his, and Chelsea's, second Europa League this decade, while it is Maurizio Sarri's first major trophy as a coach.
They will be back in the Champions League next season, but there will be no return to Europe's top table for Arsenal. Unai Emery's side had to win here to qualify, yet they were just not good enough on a bizarre night.
Emery was hoping to win this competition for the fourth time. He will get another chance next season, but for now Arsenal's 25-year wait to bring back a European trophy to north London goes on.
Chelsea will remember their evening with fondness, as will Sarri, who 24 hours earlier had stolen the headlines when he angrily stormed off the pitch here during a training session in front of the television cameras.
"Sarri is a great guy, a great coach and he deserves this," said David Luiz of his coach, who has been linked with a move to Juventus.
"The manager did amazing for this club. I don't know about speculation, now is the time to talk about the title."
The few Chelsea supporters who came will not forget their night, but the fact there were reportedly only around 1,300 in Azerbaijan will be a source of regret to those at Stamford Bridge.
UEFA's decision to play the game here had been heavily criticised, with the difficulty and cost of coming to the shores of the Caspian Sea preventing many fans from travelling and meaning Arsenal's Armenian midfielder Henrikh Mkhitaryan was controversially absent.
Hazard wants happy Chelsea ending should Madrid move materialise
Azerbaijan's President Ilham Aliyev was in the crowd, but there were thousands of empty seats in the Olympic Stadium, which holds almost 70,000,
That meant that, far away from the blood and thunder of a typical derby fixture, this had the feel of an end-of-season exhibition match on a foreign tour, for much of the first half anyway.
The players seemed short of their usual rhythm in a match played two and a half weeks after the Premier League season ended.
It came to life though, with an early moment of controversy when referee Gianluca Rocchi dismissed Arsenal appeals for a penalty as Alexandre Lacazette went down under goalkeeper Kepa Arrizabalaga's challenge.
Granit Xhaka then saw his powerful strike from 25 yards graze the crossbar as the half-hour mark approached.
Only after that did Chelsea stir, but Petr Cech -- facing his old side in his final match before retiring -- blocked Emerson Palmieri's shot and then denied Giroud at the end of a fine move.
However, as the clock ticked past midnight after a goalless first half, Chelsea went ahead when Giroud stole in front of Laurent Koscielny and stooped to head home Emerson's cross.
It was his 11th goal in this season's competition, and there was to be no comeback from Arsenal, with Chelsea quickly putting this final beyond their opponents' reach as Hazard took over.
He set up Pedro for a clipped finish low beyond Cech and into the far corner on the hour mark, and five minutes later Hazard calmly rolled in a penalty awarded after Ainsley Maitland-Niles had barged into Giroud.
Substitute Iwobi's sublime volleyed reply soon followed, but Arsenal had left themselves with too much to do, and Giroud and Hazard combined brilliantly for the latter to get his second and Chelsea's fourth in the 72nd minute.
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