Winger Ashley Young put three-times European champions United ahead just before the hour mark and Javier Hernandez extended the lead five minutes from time as they showed they meant business in a competition they would rather not be in.
Their domestic title rivals Manchester City made it harder for themselves in Portugal by conceding in the first half against the run of play before an Alvaro Pereira own goal and a late Sergio Aguero strike put them on course for the next round.
Other teams to build a solid advantage ahead of next week's second legs were Ukrainian side Metalist Kharkiv who won 4-0 at Salzburg and Atletico Madrid who take back to Spain a 3-1 win over Lazio after fighting back from a goal down.
The 2004 winners of the UEFA Cup - the Europa League's predecessor - Valencia secured a 1-0 win at Stoke City to sit pretty halfway through the tie while Twente Enschede came away with the same scoreline from Steaua Bucharest on a cold night.
Schalke 04 were glad to grab an equaliser 15 minutes from time to draw 1-1 at Viktoria Plzen, while Legia Warsaw's tie with Sporting was also evenly balanced after a 2-2 draw in Poland and Udinese and PAOK Salonika played out a 0-0 draw.
German side Hannover 96 needed an 80th-minute penalty by Jan Schlaudraff to complete a comeback at home to Club Bruges who had taken the lead early in the second half through Maxime Lestienne before Arthur Sobiech's equaliser.
Wisla Krakow, who played more than an hour with 10 men after Michal Czekaj was sent off, left it even later to snatch a 1-1 draw at home to Standard Liege with Tsvetan Genkov netting in the 88th minute.
In the day's other games, AZ Alkmaar beat Anderlecht 1-0 courtesy of Adam Maher's 35th-minute goal, Lokomotiv Moscow came from behind to overcome Athletic Bilbao 2-1 and PSV Eindhoven held on to an early two-goal lead to win 2-1 at Trabzonspor.
With the Europa League something of a consolation prize for teams who were eliminated from the elite Champions League at the group stage, the presence of heavyweights Manchester United and mega-rich Manchester City has injected it with a bit of glamour.
STRONG TEAM
Having won seven European Cups between them, United and Ajax could easily have been meeting in the Champions League rather than the Thursday sideshow.
United manager Sir Alex Ferguson, whose club have never won this competition or its predecessor, named a strong team to back up his pre-match assertions they were taking it seriously but their first-half performance lacked a cutting edge.
The English champions picked up the pace after the break and made the breakthrough when Nani's cross eventually found Young in space and the
