"Yesterday morning, we were devastated," said United midfielder Ander Herrera, dedicating the win to the victims. "But the manager told us the only thing we could do was to win this for them. That's what we've done.
"It's just a football game, just a trophy, but if we can support them with this just 1 percent, it's enough for us."
Paul Pogba scored off a deflected shot in the 18th minute - the France midfielder pointed to the sky during his celebrations - and Henrikh Mkhitaryan added a second goal in the 48th by deftly hooking home a close-range effort from a corner.
In tough circumstances, United handled the occasion better than an Ajax side featuring six players aged 21 or under and playing in the famous Dutch club's first European final in 21 years.
"I haven't seen the Ajax that I am used to," Ajax coach Peter Bosz said. "They are not used to play a final. It was all new for them."
For United coach Jose Mourinho, it was obvious that the victory was a huge weight off his shoulders, because of both the emotions of the last few days and the importance of the match. Mourinho was thrown up in the air by his coaching staff in the post-match celebrations, he rolled around on the ground with his son, and jumped up and down in frenzied fashion just before United captain Wayne Rooney lifted the trophy.
United's season was always going to be defined by this game. In Mourinho's first season at Old Trafford, he has guided the team to two trophies - the League Cup in February - and a place in next season's Champions League, the bonus prize for winning the Europa League.
"Obviously there's happiness from our achievement," Mourinho said. "But if we could, we'd change the peoples' lives for this cup. We wouldn't think twice. Does this cup make the city of Manchester a little bit happier? Maybe."
The planned pre-match one minute's silence, in honor of the victims of the blast, rapidly turned into 60 seconds of applause, during which United's fans chanted poignantly "Manchester, Manchester" for the first time. The two teams wore black armbands for the match in another mark of respect and both sets of fans came together in a show of unity, mingling happily outside the stadium and in the city center before the match.
It was billed as a clash between the efficiency of Mourinho's United against the swagger and youthful exuberance of Ajax. United was the clear winner, the players imposing themselves as much through their physicality as their superior game management.
"It was the victory for pragmatism," Mourinho said, "a victory of the humble people. People who respect their opponents and exploit their weaknesses."
For Mourinho, that meant long balls to Marouane Fellaini, a regular attacking outlet because of his height and physical presence. It meant keeping a strong defensive shape and using the pace of Marcus Rashford on the break.
Pogba - the world's most expensive player - stood out, dominating the midfield in the first half. His crucial goal had a huge element of fortune to it, though.
Fellaini laid the ball off to Pogba at the edge of the area, and the France midfielder allowed it to run across him before sending in a low left-footed shot that struck Davinson Sanchez's outstretched leg, looped up, and span into the net past wrong-footed goalkeeper Andre Onana.
Mkhitaryan's goal was much more easy on the eye. A right-wing corner was headed down by Chris Smalling, and Mkhitaryan reacted quickest with a very smart finish.
Pogba and Mkhitaryan were United's big-money signings last offseason and have had inconsistent seasons. They delivered when it mattered most.
United had little trouble keeping Ajax at bay in the closing stages and the celebrations were euphoric after the match, with Pogba producing some dance moves in front of United's jubilant fans.
It was United's sixth European trophy and the only major piece of silverware missing from its collection.
"It means the last piece in the puzzle," Mourinho said, "a club with every trophy in the world of football."
