It was probably best to file this one in the 'it's behind us' category and move on as there was precious little festive joy to be had at a chilly and wet Kingspan last night.
This was all about getting back on the appropriate track and dispelling any growing notion that all is far from well at the stadium these days. And yes they got that all-important result but this was anything but convincing.
Indeed, the western province were in with a real shout of bagging their first win in Belfast since 1960.
In the end, all that really mattered was that Neil Doak's side got what they needed, namely four points to halt what might have become a calamitous four defeats from their last five games.
For that they will be thankful even if the performance was well below standard and they appeared to ship another injury with skipper Roger Wilson leaving the field in the second half.
It didn't start well for Ulster, what with Luke Marshall out with illness and then Paddy Jackson's kick-off not seeming to have made the right contact.
Then, after the returning Ulster out-half put up a high kick, Matt Healy steamed past Craig Gilroy and linked with Darragh Leader to set Connacht on their way.
The net result was that Bundee Aki was held up on Ulster's line after several waves of green-shirted attacks but the play was called back for an earlier infringement from Ulster's scrambling defence and Jack Carty slotted the fourth minute penalty.
Ulster then got some front-foot ball after Gilroy got hold of his own high kick and after some pressure in Connacht territory which saw a lovely half-break from Darren Cave, it was the westerners who infringed. But Jackson was wide with the ninth minute penalty from out on the right.
He made no mistake five minutes later, though, after Ulster had put the squeeze on following a maul launched off a lineout. After the visitors strayed offside Jackson nailed the kick to tie the scores.
Then just before the 20 minute mark, Callum Black won a penalty on the ground and after Jackson put the ball out on the 22 metre line, Dan Tuohy claimed the lineout and Ulster attempted to maul forward. They got some momentum but then Paul Marshall fed Jackson and he hit Gilroy's angled run perfectly with an inside pass and got felled for his troubles too.
Gilroy had a lot to do and, somehow, spun through several green shirts and, against the odds, crossed the line. Jackson converted and from looking decidedly iffy in terms of their general play, Ulster had managed to take a 10-3 lead.
Jackson then missed a 26th minute penalty from reasonably close range which looked as if it could be costly, but Connacht didn't trouble the scoreboard again in the half to eat into Ulster's lead.
The opening 40 minutes ended pretty much as it had begun with the home side back-pedalling and scrambling near their line.
This time, though, despite a lovely loop run from Danie Poolman to link up with Darragh Leader, the visitors failed to make the breakthrough and coughed up a penalty in the half's final move as Ulster crowded the breakdown.
And matters hardly looked that promising in the opening exchanges of the new half with Carty's chip over the top to Dave McSharry ending up with the centre hacking the ball on and Louis Ludik having to dive on it just short of the line to retrieve a threatening looking situation which the home side then managed to clear.
Connacht then brought on Mils Muliaina but he was buried with his first touch, and then Stuart Olding threw him off in an Ulster attack which saw Dan Tuohy penalised for throwing a forward pass to Gilroy.
It was that sort of game with the error count overshadowing both sides. Olding then broke clear in the 54th minute but Jackson's cross-kick to Gilroy was taken and marked by Matt Healy despite being clattered by the Ulster winger and Connacht cleared.
And after Paul Marshall put a ball into touch near Connacht's try line, the visitors strangely went for a lone throw and but failed to get hands on it quickly enough and Roger Wilson simply emptied Carty over the line for a five-metre scrum to Ulster.
All looked set fair for a great opportunity to score but Ulster were pinged at the scrum on replacement Declan Fitzpatrick's side and the chance was blown.
Still a gilt-edged opportunity then presented itself in the 62nd minute after Connacht were done at a breakdown and Jackson stretched Ulster's lead to 13-3.
But the visitors struck next four minutes later after Gilroy was penalised for taking Healy out in the air and after Carty put the ball in the corner with a great kick, Connacht threw to Willie Faloon at the back and trundled over with second row Aly Muldowney getting the touchdown.
Carty converted and now Ulster's lead had been cut to an alarming 13-10 and Connacht, now very much with their tails up, came in waves at the home side's line.
Having lost skipper Roger Wilson to injury also didn't help with hooker John Andrew having to fill in at flanker. But when it mattered, Tuohy put a huge hit on John Muldoon who spilled the ball and Ulster won a scrum at the next breakdown to relieve the intense pressure.
It ended with Marshall booting the ball off the field and, thankfully, Ulster had held on to win.