However Ulster did not find it easy against a Connacht side who were also struggling with three straight defeats coming into the game, and it was only two tries either side of half-time which sealed the win, before Ian Humphreys' try in the last play of the game.
Humphreys had given Ulster an early lead with a penalty after just two minutes but that was cancelled out by Miah Nikora on the quarter hour.
The home side finally managed to break the deadlock as Humphreys drifted wide before switching with Craig Gilroy cutting inside and the young winger flew over for his second try of the season as Ulster led 8-3 at the break.
Connacht's hopes took a decisive hit just two minutes after the break as Ireland prop Tom Court went over, with Humphreys' conversion stretching the lead to 15-3 for the home side.
And despite a lot of effort from both sides neither was able to find a breakthrough in a scrappy second-half until Humphreys' last-gasp score.
After a period of concerted pressure the fly-half collected the ball 30 metres out and after drifting to the left he straightened and sliced through a weak Connacht defence to stroll under the posts unopposed.
His drop-kicked conversion sealed the win with the last action of the match but Brian McLaughlin's side know they will have to improve considerably ahead of the visit of Top 14 heavyweights Clermont in the opening fixture of the Heineken Cup.
Connacht will also be competing in Europe's premier competition for the first time as they welcome unbeaten Harlequins to the Sportsground.
|Ulster Rugby Score Card|
|Connacht Rugby Score Card|