Ulster (5) 21
Tries: Cave, Boss Con: Humphreys Pen: Humphreys 2, O'Connor
Edinburgh (6) 13
Try: Thompson Pens: Paterson 2 Con: Paterson
Darren Cave scores Ulster's first-half try at Ravenhill
Ulster kept their Heineken Cup hopes alive with a deserved victory at Ravenhill which ended Edinburgh's prospects in the competition.
Edinburgh failed to exploit their wind advantage as they led only 6-5 at the break as two Chris Paterson kicks were split by Darren Cave's Ulster try.
Ian Humphrey put Ulster ahead after the break and the superb Isaac Boss' 55th-minute try extended the lead to 13-6.
Jim Thompson's try gave Edinburgh hope but Ulster replied with two penalties.
The advantage of the elements suggested that Edinburgh would need to forge a double-figures lead by the interval to have a chance of winning.
Ulster had an early scare when their Ireland and Lions star Stephen Ferris appeared to twist his knee in the Ravenhill mud but he was quickly back in the action.
The home side sensed a chance after Edinburgh prop David Young's seventh-minute sin-binning but Simon Danielli wasted a chance by spilling possession when a try seemed on.
However, Ulster were cleverly running down the clock on Edinburgh's massive first-half wind advantage by holding on to possession.
Paterson did kick Edinburgh ahead in the 21st minute but Ulster were the happier outfit at that stage.
Tim Visser's run threatened the Ulster line in the 25th minute but the impressive Andrew Trimble averted the danger by nipping in ahead of Ben Cairns.
Isaac Boss shows his delight after scoring Ulster's second try
Three minutes later a try did come but it was for the home side after two wonderful darts from the lively Boss.
The scrum-half's initial charge put Edinburgh on the backfoot and after good spade work by Nigel Brady, Boss' second run allowed Dan Tuohy to set up Cave to score.
Humphreys made a splendid effort at the exceptionally difficult conversion but was inches off target.
Paterson did nudge Edinburgh ahead again with his second penalty four minutes before the break but the one-point lead looked a scant advantage ahead of the second period.
Humphreys restored Ulster's lead with a successful penalty five minutes after the break.
Boss then continued his excellent evening in the 55th evening as his clever dummy split the Edinburgh defence and enabled him to charge under the posts.
Humphreys added the extras to increase Ulster's lead 15-6.
The home side appeared in control but Edinburgh, to their credit, replied with a try of their own within five minutes as they took advantage of Ferris' sin-binning.
Thompson scored the try after taking Grieg Laidlaw's looping pass following some concerted Edinburgh pressure.
Paterson's superb conversion reduced Ulster's lead to 15-13 but Humphreys 69th-minute penalty eased home nerves and replacement Niall O'Connor added a further late penalty to deny Edinburgh a bonus point.
Ulster scrum-half Isaac Boss
"It wasn't ideal conditions but four points any which way is ideal for us.
"We worked hard in defence which also helped set up a few scoring opportunities for us.
"Hopefully, Bath or Edinburgh will do us a favour over the next two weekends.
"We've still got to show a bit more consistency. We've been a bit up and down in our performances.
Edinburgh fly-half Chris Paterson
"There was so much heart and desire in the second half but it was 40 minutes too late.
"Our first-half performance was unacceptable. Ulster controlled it particularly well into the wind but we were passive.
"The guts and effort in the second half mean nothing because we let ourselves down in the first 40 minutes."
Ulster: J Smith; A Trimble, D Cave, P Wallace, S Danielli; I Humphreys, I Boss; T Court, N Brady, BJ Botha; D Tuohy, E O'Donoghue; S Ferris, D Pollock, C Henry (capt).
Replacements: N O'Connor for Humphreys 72, B Young for Court 62, A Kyriacou for Brady 62, D Fitzpatrick for Botha 75, Caldwell for Tuohy 72.
Not Used: Anderson, Willis, Nagusa.
Edinburgh: C Paterson (capt), J Thompson, B Cairns, J Houston, T Visser, P Godman, G Laidlaw, A Jacobsen, R Ford, D Young, S MacLeod, J Hamilton, S Newlands, A MacDonald, R Grant
Replacements: N De Luca for Cairns 50, M Robertson for Visser 65, R Samson for Laidlaw 70, A Kelly for Ford 71, C Hamilton for MacLeod 69.
Not Used: K Traynor, G Cross, D Callam.