The Reds, crowned champions on Monday, showed signs of tiredness towards the end and conceded an injury-time equaliser to Nathan Eccleston after Michael Ngoo pulled one back on 49 minutes.
There were few openings in a tight first half although former Reds trialist Ngoo caused a few problems with his awkward running style. Sam Johnstone wasn't extended in the opening 45 minutes, however, and the visitors were clinical when allowed a sniff of goal at the other end.
Lingard's low free-kick was not dealt with by the Liverpool defence and Michael Keane pounced from a couple of yards out to deflect the ball home for his fifth goal of the domestic campaign. Four minutes before the interval, the roles were reversed as Michael Keane launched a glorious through ball into the path of Lingard, who showed his usual composure to clip a confident finish past the advancing Peter Gulacsi.
The second period started in driving rain and Ngoo gave the hosts hope when United were caught napping at a throw-in and the leggy striker was able to tap in from close range. Buoyed by the breakthrough, the Merseysiders went close when Johnstone helped a Suso drive on its way over the bar and Ngoo dropped a header wide.
There was controversy when the Reds were denied a penalty when a free-kick by skipper Davide Petrucci appeared to strike a hand in the wall, possibly Conor Coady's, inside the area and the decision to play on left the game in the balance.
Subsitute striker Eccleston fired off target from a difficult angle and Suso shrugged off Ezekiel Fryers but curled wide after skipping past