The Broncos looked slick in attack and pounced again as Kodi Nikorima broke the line and found a flying Roberts with a perfect grubber to gift the superstar centre another try for 2017.
The onslaught continued minutes later when Brisbane winger Jordan Kahu easily outleapt opposite number Antonio Winterstein, making the visitors' advantage 14-0 after just 12 minutes.
North Queensland hit back with the try they so desperately needed with Morgan finding Maroons teammate Gavin Cooper with a great ball close to the line.
Ethan Lowe's conversion cut the Broncos' lead to eight and Brisbane had even more to worry about when Boyd picked up a hamstring strain while fielding a kick on the final play of the half.
Cowboys utility Ben Hampton was denied the second half's first try when he was held up over the line and while the Cowboys enjoyed a number of repeat sets the Broncos defence answered all questions asked of them.
Brisbane's injury woes continued when Alex Glenn left the field for a head injury assessment but the Broncos were able to mount pressure through Ben Hunt's kicking game.
Their extended possession paid off when prop Adam Blair barged his way over for a crucial four-pointer.