But Lukaku’s emphatic finish in the 88th minute was enough for all three points, even though Paul Pogba missed an injury-time penalty.
Lukaku was twice denied by Angus Gunn in the first five minutes, although United’s early rhythm was disrupted by treatment on a Scott McTominay head injury.
Jannik Vestergaard headed over when picked out unmarked from a corner, and Ryan Bertrand was angry not to win a penalty from a shirt pull by Chris Smalling.
Saints’ increasing pressure told 26 minutes in, when Valery’s ferocious strike from 25 yards beat David de Gea at his left-hand post, even though he got hands to the ball.
United were struggling to impose themselves and suffered a further blow when Sanchez had to go off with a knee injury seven minutes after the restart.
However, they turned the scoreline around in a spectacular six-minute spell. First, Pereira curled a spectacular strike beyond Gunn from 25 yards out, before Lukaku got free in the box, cut onto his right foot and drilled a shot into the bottom-right corner.
Just as United appeared to be heading for victory, Ward-Prowse sent an unstoppable effort beyond De Gea to send the travelling fans into raptures and silence the home fans.
But with two minutes of normal time remaining, Lukaku curled another low right-foot strike from outside the box past Gunn, prompting further cries of ‘Ole, Ole, Ole’ from the Stretford End, which were only slightly dampened when Gunn kicked away Pogba’s penalty.