Following a disappointing first half, the Reds scored twice in quick succession after the interval through teenager Henriquez and Bebe to set up a hard-fought victory against the Conference outfit.
County were quickly into their stride and almost took an early lead. Nick Powell had to head Danny O'Donnell's goalbound effort off the line and Tom Eckersley also failed to connect properly during a nervous opening for the visitors.
Bebe lashed into the side-netting and Powell clipped an ambitious attempt off target but Stockport went close again when Tom Collins got the better of Tyler Blackett and forced a good stop out of Jonny Sutherland before firing a second opportunity wide.
Warren Joyce's side struggled to find any attacking rhythm and were not helped by Powell limping off before the break after failing to shrug off a knock. Adnan Januzaj, one of three Belgians in the starting line-up, sailed a free-kick into Lewis King's hands but there were few scares for the keeper in the first half.
Andy Graham had Sutherland flying across his goal with a fine attempt from long range but United soon assumed total control with two goals inside a couple of minutes. Federico Macheda burst into life when collecting a Charni Ekangamene pass and fed Henriquez with the Chilean taking advantage of the fact he was afforded too much space on the edge of the box to drill home a cool finish.
Macheda and Henriquez were also involved in the move that led to the second goal as Bebe took