Goals from Tom Cleverley, Febian Brandy and Rodrigo Possebon gave United victory despite some good pressure from the hosts, who pulled a late goal back through David Brookes.
It took just seven minutes for Cleverley to notch the first goal of the Solskjaer regime, turning smartly and firing home from 15 yards.
Although the hosts rallied well, Brandy doubled the Reds' advantage just before the interval when he fired past Burscough keeper Ian Lowe.
Fifteen minutes after the interval, Possebon put the game to bed with a stunning goal. Picking the ball up 25 yards from goal, the Brazilian midfielder smashed a superb dipping effort into the corner of the goal.
Although the Reds dominated the remainder of the game, Brookes had the final say when he slipped the ball under Sam Johnston to salvage some rewards for the hosts' spirited performance.
The Reserves' next outing is on Saturday, 19 July, when the Reds travel to near-neighbours Altrincham.