The Spanish club came from behind to defeat its English opponent 3-1 at the St. Jakob-Park stadium in Basel, Switzerland, with Kevin Gameiro canceling out Daniel Sturridge's beautifully controlled first half strike before a brace from Coke sealed Sevilla's success.
There was controversy over Coke's second goal on 70 minutes with Liverpool players claiming the Sevilla captain was offside before firing beyond goalkeeper Simon Mignolet.
While the linesman did initially raise his flag that decision was promptly over-ruled by referee Jonas Eriksson who recognized that the ball had deflected off Liverpool midfielder Philippe Coutinho into Coke's path, thus rendering the Sevilla player onside.
Liverpool players complained bitterly but the officials made the correct decision despite the initial confusion.
In spite of that controversy, however, Sevilla was fully deserving of its two goal winning margin.
The victory marks Sevilla's fifth Europa League success in 11 years and ensures it will qualify for next season's Champions League.
Liverpool, meanwhile, will miss out on European competition altogether next year having finished a poor eighth in the English Premier League this season.
"We didn't do ourselves justice," a disappointed Liverpool midfielder, James Milner, told BT Sport on the pitch after the match.
"We didn't think about the Champions League, it was about winning this trophy. We didn't manage to get over the line," Milner added.
Liverpool boss, Jurgen Klopp was equally disappointed. The German coach has now experienced five straight losses in major finals and pointed to a lack of belief in his players as reason for their poor second half showing.
"The start I was not happy with, but we scored a wonderful goal. What happened after (Sevilla's equalizer) is the problem," he said.
"We lost faith completely in our style of play. We lost shape and we were nervous in defense. That shows our development is not as good as hoped."
For Sevilla, thoughts of its rival's misfortunes were of little concern as ecstatic players danced and celebrated wildly in front of fans.
The Spanish side has taken near exclusive ownership of the Europa League trophy in recent years.
It racked-up back-to-back triumphs in 2014 and 2015, mirroring repeat UEFA Cup successes (the previous incarnation of the Europa League) achieved in 2006 and 2007.
Wednesday's victory also means Sevilla extends its record as the most successful club in Europa League history. It's five triumphs are two more than Juventus, Inter Milan and Liverpool which are all tied on three apiece.
"We suffered a lot today, we've suffered all season," said man-of-the-match Coke in comments carried by the official UEFA website after the match.
"When the game was most difficult and everything was looking uphill we showed that this team has courage and fighting spirit," he continued.
Sevilla's sporting director, Monchi, echoed Coke's sentiments: "I'm lost for words. This is very difficult, but a huge achievement. The fans helped us a lot. I'm proud to be a Sevillista."
The only blot on a near perfect evening for Sevilla was clashes close to the area housing its supporters inside the stadium before the game.
Scuffles briefly broke out after rival fans confronted each other but order was quickly restored by police.
Liverpool fans significantly outnumbered their Spanish counterparts and it appeared there was little segregation until police were forced to intervene.
Fortunately the violence didn't flare up again throughout the match and Sevilla fans were able to freely celebrate their side's success on the full-time whistle.