The South Korean, who looked sharp from the first whistle, made a telling contribution as United took the lead in the sixth minute. Park's interception of a cross-field pass redirected the ball to Berbatov, who quickly released Chicharito. The Mexican shimmied away from Toby Alderweireld and arrowed a left-footed finish past the helpless Vermeer.
Another United counter-attack almost yielded a second goal in the 15th minute, as Fabio neatly won possession and burst forward before releasing Chicharito, whose sliding ball across the area was hooked away from the lurking Berbatov by Jan Vertonghen.
Ajax's noteworthy ripostes invariably involved the highly-rated Christian Eriksen. The Danish youngster had already had one 20-yard effort deflected narrowly wide before his surging run teed up Miralem Sulejmani, only for the Serbian to blaze over the bar.
Siem de Jong burst infield and scuffed a shot wide before Aras Ozbiliz drew a smart catch from David De Gea with a neat turn and shot, as the visitors sought to haul themselves back in the tie.
Inevitably, United's counter-attacking menace also spawned openings. A crafty reverse-ball from Nani released Berbatov but, as he bore down on goal, the Bulgarian attempted to square to Chicharito instead of going for goal himself, and Alderweireld was able to deflect the ball clear.
The hosts would soon rue that spurned chance to bury the tie. With eight minutes of the first period remaining, a sustained period of Ajax pressure culminated in Siem de Jong teeing up Ozbiliz just outside the area, and the Turk's shot rocketed past De Gea, via a slight deflection off Jones.
Though there was a hint of handball by Lodeiro in the build-up to the equaliser, United could only reflect on spurned chances to end the tie.