Another triumph next week against Castres will secure a home quarter-final for Mark Anscombe's side.
A first-half try from Nick Williams along with late second-half scores by Jared Payne and Darren Cave secured the four points and with Northampton beating Castres, Ulster progressed after a scrappy game played in difficult conditions at Ravenhill.
The match left the injury-hit Warriors - who were unable to have two prop replacements on their bench - without a win in a miserable season in Europe.
Northampton battled hard for an 18-12 victory over Castres that keeps them in the hunt for quarter-final qualification.
Northampton could still reach the knockout stages as one of the best group stage runners-up.
In bitterly cold temperatures and through thickening fog at Franklin's Gardens, Northampton ground out the victory they needed with three penalties each from Stephen Myler and Ryan Lamb.
The Saints will now go in search of a bonus-point victory over Glasgow next weekend and hope that is enough to secure a berth in the quarter-finals.
Aviva Premiership strugglers Sale suffered a fourth consecutive defeat by French opposition in the Heineken Cup as Montpellier kept alive their qualification hopes with a 27-16 bonus-point win at the City of Salford Stadium.
With their quarter-final hopes sunk in December by back-to-back defeats to Toulon, Sharks director of rugby Steve Diamond opted to give run-outs to several fringe players and, as expected, they proved no match for their star-studded visitors.
It proved to be a testing debut for number eight Josh Beaumont, the 20-year-old son of former England captain Bill Beaumont, who found himself up against man-of-the-match Johnnie Beattie.
Montpellier, flying high in the French League, made it four successive wins while a bonus point enabled them to draw level with Toulon, who play Cardiff on Saturday before hosting their pool six rivals at Stade Yves du Manoir in their final match next Saturday.