In the team's 64th and final match of a gruelling campaign, it completed the set of major honours for the Reds, and sealed an automatic place in the Champions League group stage next season.
This was also a victory for the city and people of Manchester, coming just 48 hours after the tragic events in which 22 people were killed by a suicide bomber at the Arena on Monday.
The build-up to the game had been overshadowed by the terrible atrocity, with the match preceded with a minute's silence and then applause as both teams donned black armbands.
Ajax started nervously and almost gifted United the lead inside a minute when Andre Onana fumbled and Paul Pogba flashed a volley wide.
Juan Mata's cross narrowly evaded the onrushing Marouane Fellaini and Sergio Romero had to be alert to keep out Bertrand Traore at the other end.
United's early dominance paid dividends as we went ahead on 18 minutes with Pogba - impressive throughout - again heavily involved.
Mata found Fellaini whom in turn picked out Pogba and his 25-yarder looped over a back-pedalling Onana with the aid of a heavy deflection off Davinson Sanchez.
Five minutes before the break, Antonio Valencia burst clear down the right and saw his angled effort beaten away by the Ajax keeper.
United began the second half as they had ended the first and moved 2-0 ahead three minutes after the restart as Henrikh Mkhitaryan made history.
The Armenian hooked home Chris Smalling's flick on from a Mata corner for his fifth European away goal of the season - the highest such tally from a United player in a single campaign.
Fellaini headed straight at Onana and Jesse Lingard slipped when clean through having been played in by fellow substitute Anthony Martial late on.
'Manchester, Manchester, Manchester' echoed around the Friends Arena in the closing stages as the 9,000 travelling Reds magnificently and poignantly backed the team throughout.
There was to be no late twist in the tale this time as United saw out the match in relative comfort to complete the set of major honours and provide a fitting tribute to the grief-stricken people of their city.
Overall team performance: 8/10
United Faithful Man of the Match: A superb all round team performance inspired by world record signing Paul Pogba who helped his side dominate and control the match.