Ulster got back to winning ways in the Guinness PRO12 and moved up one place to fourth but they were made to scrap every inch of the way by Connacht on Boxing Day.
Pat Lam's visitors could have even snatched their first win in Belfast since 1960, but a tight and fairly dire affair ended 13-10 in the hosts' favour.
The entire game on a wet and cold night saw just two tries, with Ulster winger Craig Gilroy getting over in the first half and then Connacht second row Aly Muldowney crashing over in the second 40 minutes.
Ulster had led 10-3 at the break, but the westerners came back and, although they made off with a losing bonus point, will be rightly disappointed at not getting more from this one in a game which saw both sides missing front-line Ireland players who had been rested.
The result halted Ulster's losing run of having been beaten in three of their previous four games, and got Neil Doak's men back on track towards their aim of making the play-offs - even though the performance was well short of where it should have been.
Connacht were out of the blocks first on another typically rainy night at the Kingspan, and Jack Carty nailed a fourth-minute penalty after the visitors had countered well from a Paddy Jackson high kick.
The scores were then tied just before the 15-minute mark when Jackson slotted a penalty.
Ulster launched a line-out maul four minutes later after winning a penalty and from this Jackson threw a wonderfully timed inside pass to winger Gilroy, who managed to spin his way through some weak Connacht tackling to cross the line.
Jackson converted and Ulster had earned themselves a 10-3 lead, which really should have been 13-3 in the 26th minute but Jackson was off target with a penalty.
Neither side scored in the remainder of the half, with Ulster defending their line right at the end of the opening 40 minutes and winning a penalty as Connacht expended a great deal of energy only to come away with nothing.
The second half was largely a slog-fest as the weather worsened and the error rate spiralled, but the stalemate was finally broken when a gilt-edged opportunity presented itself in the 62nd minute after Connacht were undone 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 Matt Healy out in the air and, after Jack 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 Muldowney getting the touchdown.
Carty converted to cut Ulster's lead to three points, but there were no further points scored - despite both sides applying some pressure towards the end.