Mark Warburton’s side scored three goals in eight minutes through substitute Lydon Dykes (53, 59) and Moses Odubajo (58) to leave the home fans in party mood.
Substitute Anthony Elanga pulled a goal back for the visitors, but it only proved to be a consolation as Solskjaer and his team were handed a significant wake-up call ahead of the new Premier League campaign.
In what was a frantic opening to the game, Mason Greenwood’s pass reached Facundo Pellistri and the Uruguayan’s touch took the ball into the path of Lingard. The England international only had Seny Dieng to beat and made no mistake from close range.
The lead did not last long, however, as QPR, backed by their enthusiastic home support, responded four minutes later. Lee Wallace’s inch-perfect cross picked out an unmarked Austin, and the QPR striker made no mistake, heading past Tom Heaton.
QPR, who announced the permanent signing of midfielder Stefan Johansen from Fulham ahead of kick-off, grew from that moment and looked the sharper of the two sides as they dominated much of the rest of the first half.
Brandon Williams had to be alert, turning the ball behind with Austin waiting to pounce at the far post before Heaton comfortably saved Jordy de Wijs’ header.
However, despite QPR’s impressive half, they almost gifted United the lead just before the break. Lingard pounced on a ball and but for Robert Dickie’s perfectly timed challenge, the forward had a clear route to goal.
Both sides made changes at the break and it was Dykes who made an instant impact, turning home Wallace’s cut back to continue QPR’s dominance.
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It just kept getting better and better for the hosts as Odubajo cut in from the left before smashing a left-footed strike past Lee Grant and into the top corner of the net.
The scoring spree was rounded off a minute later. Moments after Joe Walsh had denied Elanga, Dykes also cut in off the right before picking out the bottom corner with a left-footed strike.