They are now up to eighth in the table but they were made to work hard against a well drilled Blues side who led 6-0 early on after two Jarrod Evans penalties.
But the introduction of Sam Davies at half time for the injured Dan Biggar turned the game for the Ospreys and Rees - whose side impressed last Sunday in defeat to Clermont Auvergne in Europe - was pleased with the result.
"We are pleased to get the win, after the week we are coming on the back of," he said.
"The four points is just huge in terms of getting through these fixtures and manage the group from week to week.
"The performance was scratchy at times, we had to adapt in the game to some pretty smart Blues defence, they were good around the contact area but filled the field as well so we were a bit misplaced at times.
"We had to smarten up and cut our cloth accordingly. It was about building the pressure, not getting het up about the scoreboard.
"It was not our intention to play that sort of game we wanted to open up early but they caused us umpteen issues.
"We were not as free-flowing for that, but we had to adapt and ultimately put in a performance to get the four points - especially from 6-0 down."
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