Wales’ Capital Region hadn’t registered a win at Belfast since 2010, but took a two-point lead into the interval thanks to Morgan and Dacey and had further opportunities.
However, they were unable to add to their tally and a series of fortuitous calls saw the hosts wrestle their way back into proceedings with John Cooney slotting a pair of penalties to snatch the spoils.
The ever-reliable boot of Cooney opened the scoring for the hosts, striking a long-range effort between the sticks with only two minutes on the clock.
Up against a stern Ulster defence, the visitors were forced to remain patient with the ball in-hand.
Jason Harries made a dangerous break into the 22, but the home side recovered well, eventually forcing Samu Manoa to knock on from an attempted offload.
Billy Burns looked to unlock the Cardiff Blues defence with a threatening chip behind, but Harri Millard, making his first Championship start, recovered well to gather.
Moments later, the youngster found himself in space out wide, after a fine offload from midfield partner, Rey Lee-Lo.
The centre kicked ahead, and despite Cooney being on-hand to gather the loose ball, the chase was good enough to see Millard and Scully combine to put the scrum-half in touch, deep inside his own 22.
The ball was secured at the line-out and, following a few bruising carries from the forwards, a long pass from Jarrod Evans put Morgan in at the corner for the game’s opening try.
Five minutes later, Ulster struck back with a try of their own. Stuart McCloskey paved the way with a quick tap, and his offload bounced off the shin of Kieran Treadwell, in support. The lock had enough in the tank to win the footrace and touch down.
Cooney converted, but the lead didn’t last long, as Wales’ Capital Region responded positively. Once again, it was a line-out inside the Ulster 22 that set-up the platform.
Despite the home defence initially dealing with the pressure, the visitors were awarded a penalty, with Evans putting the ball into the corner.
This time, the drive proved to be effective, as Dacey powered over for his second try in as many games. Outside half, Evans, cooly slotted the conversion to put the Welsh region ahead.
A fine move in midfield allowed Harries to kick ahead into the Ulster 22, and once again Scully’s chase forced the cover-defence into touch, however, it was opportunity missed this time as the hosts forced a turn-over at the resulting set-piece.
A heroic defensive set denied Ulster a way back into the game, as impressive line-speed from the visitors saw the hosts forced back outside the 22.
Richard Hodges would’ve been pleased with his side at the break as they nullified another promising opportunity for Ulster on the brink of half time.
Mulvihill’s side led by two points at the interval, and almost streched their lead within a minute of the restart.
Evans’ clever kick through was fathered by Millard, but promising full back, Michael Lowry, was on-hand to make a try-saving tackle.
The alarm bells were ringing when James Hume made a break from his own half, but his attempted offload found the hands of Blaine Scully, to quell the danger.
Dillon Lewis impressed on the floor, winning a trademark turnover within a minute of being introduced into the game.
However, the hosts were slowly wrestling their way back into the game, and found themselves with a man advantage, as Seb Davies was harshly sent to the sin bin for a clear out.
This allowed Ulster to regain the lead through the boot of Cooney, heading towards the final quarter of the match.
A moment of magic from Morgan almost gave his side a crucial score. The full back found replacement Tomos Williams on his outside, but the scrum-half’s attempted offload to Harries was judged to have been knocked on.
Television replays showed the ball had in fact been slapped out of Williams’ hands and Ulster had got themselves out of jail once more.
Cooney added another penalty for Ulster to open up a four-point lead but Cardiff Blues had further opportunities.
Another break, first from Morgan and then Smith laid the platform for their side to surge into the red zone with just four minutes remaining. They hammered at the try-line but were penalised when Rory Best forced a turnover, despite appearing off his feet.
The Blues continued to challenge in the closing stages but they were unable to manufacture a score as Ulster clung on for the spoils.