Hazard has been strongly linked with a move away from Chelsea this summer
Eden Hazard scored the winning penalty as Chelsea edged past Eintracht Frankfurt 4-3 on penalties to set up an all-English Europa League final against Arsenal.
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.
With the score 1-1 after the first leg, Chelsea took lead in the second when Ruben Loftus-Cheek coolly stroked into the far corner in the 28th minute, but the night was far from straight-forward.
Frankfurt levelled the tie four minutes after half-time when Luka Jovic slotted past Arrizabalaga after being played in by Mijat Gacinovic.
Jovic's goal punished Chelsea for a sloppy start to the second half and the Blues continued to be wasteful as Stamford Bridge became increasingly restless.
In extra-time the Germans twice had efforts cleared off the line with David Luiz first denying Sebastian Haller and then Davide Zappacosta clearing Haller again at a corner.
Chelsea thought they had won it late in extra-time but Cesar Azpilicueta, who later missed first in the penalty shootout, had a goal ruled out when the referee deemed he had bundled the ball out of Frankfurt keeper Kevin Trapp's hands.
Redemption for Arrizabalaga and Hazard's perfect farewell?Arrizabalaga saved two Frankfurt penalties in the shootout
The shootout was Chelsea's first since they lost the Carabao Cup final to Manchester City on penalties in February.
That game was overshadowed by Arrizabalaga's refusal to be substituted, but at Stamford Bridge he proved to be the hero.
After Azpilicueta missed first, Arrizabalaga remarkably kept out Eintracht's fourth penalty by trapping the ball under his shin as he stood still when Hinteregger went for power and then dived low to his right to palm away the visitors' fifth.
That left Hazard with the opportunity to complete the win and the Belgian delivered - sending Trapp the wrong way, tucking the ball into the corner.
Hazard has been strongly linked with a move to Real Madrid this summer and if he does depart the game will be his final at Stamford Bridge after seven years at the club.
There were no waves to the crowd or clear indications he will leave in the summer and when asked whether the final would be his last game for the club he said "in my mind I do not know yet".
If he does leave in the summer it would be a fitting way for him to finish in west London.
Sarri to end difficult season on a high?
The win also means Chelsea have a final chance to earn silverware in Maurizio Sarri's first season in charge.
Like campaign as a whole, the night was far from smooth for the Italian and had difficult moments.
He become increasingly frantic on the touchline as his side lost control of the game in the second half and his decision to remove goal scorer Loftus-Cheek when bringing on Ross Barkley late on was loudly booed by the Chelsea fans.
But for all of the season's problems, including the Arrizabalaga affair and protests from fans against his style of play, Chelsea are quietly achieving their pre-season aims at the end of the season.
Last weekend they secured a top four finish and Champions League qualification through their league position and are now into their first European final since winning the Europa League in 2013.
Result harsh on impressive EintrachtLuka Jovic is the joint top scorer in the Europa League this season alongside Chelsea's Olivier Giroud with 10 goals
Had either of their efforts cleared off the line in extra time gone in, it would have been hard to argue Eintracht Frankfurt were not worthy finalists.
Over the two legs German side, fancied by few at the start of the competition, had opportunities to seal a first European final since 1980.
Rather than sitting back after Jovic's equaliser - the highly sought after 21-year-old's 10th Europa League goal of the season - they continued to attack Chelsea in the second half and the tension around Stamford Bridge was clear.
Substitute Haller should have scored his first chance in extra time but failed to make proper contact with his volley, kicking the ball into the ground with his studs rather than side-footing into the net, and that allowed Luiz to clear.
The visitors were roared on by their vocal travelling support, some of whom were in tears at the end of the penalty shootout.
Despite the disappointment those fans chanted in support of their team long after the final whistle as the players and backroom staff emotionally came together and linked arms in front of the away end.
Chelsea' home shootout run - the best stats
Chelsea have won each of their last four penalty shootouts at Stamford Bridge, with this their first in European competition at home.This is the first time that all four places in the Champions League/European Cup and Europa League/UEFA Cup finals will be filled by one country.Chelsea have reached their first major European final since the 2013 Europa League, when they beat Benfica 2-1 under manager Rafael Benitez.Chelsea have never lost a home game against German opponents in all competitions (W7 D3).Eintracht Frankfurt have only lost one of their last nine away Europa League games (W5 D3). The German side have scored in all seven of their games on the road in the competition this season.Luka Jovic has scored 10 goals in the Europa League this season; no player has netted more (level with Olivier Giroud).Chelsea forward Eden Hazard has had a hand in 24 goals in 26 appearances at Stamford Bridge in 2018-19 (13 goals, 11 assists). Ruben Loftus-Cheek has been directly involved in nine goals in his last 14 appearances for Chelsea (4 goals, 5 assists); as many as in his previous 45 games for the Blues.'We got into trouble' - Sarri reaction
Speaking to BT Sport, Chelsea boss Maurizio Sarri said: "I think we played a very good first half and then we got into trouble after the break. We conceded a goal in 10 minutes of panic.
"We were better in the last part of the match but we were tired in extra time and it was difficult.
"We started with three injuries and picked up two more during the match after we lost Andreas Christensen and Ruben Loftus-Cheek, so it wasn't easy but we are now in the final."
