Kieron Dawson, Carlo Del Fava and Roger Wilson all touched down in the final half-hour as Ulster took the honours by 30-13 in Friday's basement battle in Galway.
In caretaker coach Steve Williams' second game in charge, Ulster managed to lift themselves off the bottom of the table and above Friday's hosts Connacht as they struck an important blow in the context of qualifying for next season's European Cup.
A 50th-minute try from Danny Riordan edged Connacht into a 10-6 lead but Ulster came good with fly-half Paddy Wallace landing six out of seven kicks as part of a man-of-the-match performance.
With both camps viewing this Sportsground encounter as their most important match of the season, an error-strewn first half was predictable.
The early collisions were ferocious as both provinces looked for the upper hand in the cold, crisp conditions.
Connacht's Ireland international duo Johnny O'Connor and Gavin Duffy both made early impressions, the former at the breakdown and the latter with the boot, but Ulster were first off the mark.
Wallace landed a sixth-minute penalty to open the scoring after O'Connor was pinged for offside.
Although they had the lion's share of possession, Ulster were guilty of too many errors as they fluffed numerous attacking opportunities.
Connacht were also disappointingly limited in attack and apart from putting Mel Deane through on crash ball, the westerners seemed unwilling to mix things up, despite having the likes of Riordan and Aidan Wynne out wide.
The game was cramped between the 22s until late in the half when Ulster threatened to make a breakthrough. That bout of pressure led to a second successful penalty for Wallace, who punished Adrian Flavin for a 33rd-minute ruck infringement.
But a late lapse in concentration from the visitors allowed Connacht to hit back in injury-time - Ulster were penalised for taking a man out in the lineout and Tim Donnelly chipped over from 30 metres out.
Connacht, 6-3 down at the break, managed to take the lead immediately after Ulster flanker Neil Best was sin-binned for a deliberate knock-on.
Their try had a good deal of fortune about it but Riordan took his chance well as he collected the ball and raced clear after a John Muldoon kick had deflected off Ulster's Mark Bartholomeusz and into the Connacht number 13's grasp.
Donnelly converted but Ulster hit back three minutes later when a lineout take from Matt McCullough and pop pass from Isaac Boss sent flanker Dawson on an arcing 15-metre run which saw him cross in the right corner.
Wallace knocked the conversion in off the post and while lively replacement Andy Dunne briefly levelled at 13-13, Wallace's 57th-minute penalty nudged Ulster back in front.
Connacht huffed and puffed but were lacking that killer pass and Ulster gleefully closed out their first win in all competitions since September.
Del Fava dived over after Wallace had made use of numbers out wide on the left and, in the first minute of injury-time, good work from Simon Danielli and Tommy Bowe sent Wilson storming over in the same corner.
Peter O'Mahony was named man of the match against England last month
21 April 2017, 7:22pm
Peter O'Mahony's performance in the RBS 6 Nations finale for Ireland against England was crucial to his selection for the British & Irish Lions on Wednesday, Ireland and Lions defence coach Andy Farrell has revealed.