Hazard, who could have played his final game for the Blues at Stamford Bridge, converted after Chelsea goalkeeper Kepa Arrizabalaga had saved from both Martin Hinteregger and Goncalo Paciencia.
Chelsea will now meet Arsenal in the final in Baku on 29 May and the result means both the Champions League and Europa League final will be played between English clubs this season – the first time all four finalists in Europe’s top two competitions have come from one nation.
In the other semi-final Pierre-Emerick Aubameyang’s hat-trick for Arsenal sent them to the final against Chelsea as they won in Valencia for a 7-3 aggregate victory.
The Gunners are now one win away from Champions League qualification, while manager Unai Emery can make history by winning a record fourth Europa League crown.
Trailing 3-1 from the first leg in London, Kevin Gameiro’s close-range effort had given the hosts the early impetus.
However, Aubameyang’s right-foot volley from 20 yards levelled matters before Alexandre Lacazette put Arsenal ahead with a placed effort into the right corner.
Gameiro, a four-time winner of the competition at Sevilla and Atletico Madrid, tapped in Valencia’s second of the night before Aubameyang rounded off the scoring.
The Gabon forward slid in from Ainsley Maitland-Niles’ cross and then blasted emphatically into the top corner late on to complete his hat-trick and a 4-2 win.
It means Arsenal, whose first away game of this Europa League campaign was in Azerbaijan against FK Qarabag, will return to the country to face Maurizio Sarri’s side in the final on Wednesday, 29 May (20:00 BST).
It will be the first all-English affair since Tottenham defeated Wolves over two legs in 1972, when the competition was known as the Uefa Cup – and the first time that all four finalists in Europe’s top two club competitions have come from one nation.