Despite trailing 6-0 inside 13 minutes, the visitors ran out comfortable 21-6 winners courtesy of tries from no.8 Reuban Tucker and left wing Harry Robinson.
Morgan, who helped himself to 22 points in the Ospreys 37-12 victory in North Wales two weeks ago, kicked two penalties early on to suggest that it would be the Ospreys who made it three successive victories in the championship this term.
However, Blues outside half Joseff Griffin halved the deficit after 19 minutes and on the half hour, Tucker nipped in for a try Griffin failed to improve.
The excellent pivot made up for that miss with a second penalty, a minute later, and two minutes before the interval, Robinson crossed for his first try of the season.
Griffin converted and added a penalty 10 minutes into the second half to make sure of another outstanding win for a competent looking Blues side.
Team manager Sophie Bennett said; "It was another decent performance although in terms of developing, there is plenty to work on.
"We can now look forward to a tough game against Sale on the 20th before stepping back into the Championship for our game against the Dragons."