United edged into the last 16 of the Europa League by virtue of last week's clinical victory in Amsterdam, as Ajax earned a deserved second leg victory at Old Trafford.
Chicharito capped a swift United breakaway to open the scoring in the sixth minute, only for the visitors to hit back and level before the break through Aras Ozbiliz's 20-yard effort.
The visitors went for broke after the interval, and had United on the ropes for a 10-minute period in which David De Gea produced a wonderful, point-blank save to deny Siem de Jong.
Nerves were set jangling with three minutes remaining when the unmarked Toby Alderweireld powered home a header from Ozbiliz's free-kick, but the Reds withstood the visitors' late pressure to squeak into the next round, where Athletic Bilbao await.
United's starting line-up featured four changes to that which had won in Amsterdam a week earlier, as Rafael Chris Smalling, Ji-sung Park and Dimitar Berbaov replaced Rio Ferdinand, Jonny Evans, Michael Carrick and Wayne Rooney respectively. Ferdinand's absence meant Phil Jones moved into central defence, while Ji-sung Park skippered the side.
Ajax, with a two-goal deficit to overturn, reprised their 4-3-3 approach with two changes from the side beaten a week earlier; as Nicolas Lodeiro and Ricardo van Rhijn stepped in for Ismail Aissati and the injured Dmitri Bulykin.