Ulster edged out a battling Edinburgh outfit in Friday's Celtic League game.
Ulster (13) 36:
Tries: Maggs, Steinmetz, Bowe, Frost.
Con: Steinmetz 2.
Pens: Humphreys 3, Steinmetz.
Edinburgh (13) 34:
Tries: Boston, Hogg, Lee, Callan.
Con: Laney 4.
Pens: Laney 2.
Tries from Kevin Maggs and Paul Steinmetz helped Ulster lead 13-0 but a Paul Boston try and three Brendan Laney kicks levelled the game by half-time.
Third quarter tries from Alistair Hogg and Derrick Lee then helped Edinburgh into a 27-22 lead at Ravenhill.
However, touchdowns by Tommy Bowe and Rowan Frost put Ulster ahead again and David Callam's converted try came too late for the visitors.
In an error-strewn first half, Ulster initially held the advantage before the visitors came storming back.
Humphreys kicked Ulster ahead in the eighth minute with a 30-metre effort after Edinburgh had infringed at a ruck.
The home team stormed further ahead in the 16th minute when Maggs took a short pass from Kieran Campbell to crash over.
Ulster's second try came in the 22nd when Tyrone Howe bolted down the left wing, kicked ahead and after Bryn Cunningham had hacked through, Paul Steinmetz dived over for the touchdown.
Edinburgh struck back almost immediately when poor Ulster defence allowed Laney to make a half-break for centre Paul Boston to scoot through a big gap to score under the posts.
Campbell Feather (right) scored one of Ulster's four tries
Laney converted and then landed a penalty from 30 metres as Ulster failed to clear their lines and were penalised at a ruck.
The Edinburgh fly-half then brought the sides level in the 36th minute with his second penalty.
Humphreys edged Ulster in front again two minutes after the restart with his second penalty but he then presented the visitors with their second try in the 49th minute.
The Ireland international's looping pass was intercepted by number eight Hogg who galloped 50 metres go under the posts with Laney adding the extra points.
Humphreys narrowed the gap to a point with his third penalty in the 57th minute but he was not having one of his better days with the boot and Paul Steinmetz was then given the kicking duties.
Steinmetz immediately gave Ulster the lead in the 63rd minute but the home side immediately gave away another soft try in the 67th minute when full-back Lee was put away to run in under the posts for Laney to again convert.
But back came Ulster again a minute later to level with Steinmetz cutting through to put Bowe in midway out and the centre's conversion put Ulster into the lead again.
Replacement Frost grabbed Ulster's fourth try and important bonus point when he was driven over from a line-out with Steinmetz adding the extra points.
Back came Edinburgh with their fourth try and a second bonus point when replacement David Callam crashing after they turned an Ulster scrum and Laney's conversion made for an exciting climax.
But Ulster held out to move up the table with their first five-pointer of the season.
Ulster: Cunningham, Bowe, Maggs, Steinmetz, Howe, Humphreys, Campbell, McCormack, Shields, Moore, Longwell, McCullough, Feather, capt, Pfister, Wilson.
Replacements: R Best, S Best, Frost, Mustchin, Doak, Larkin, Maxwell.
Edinburgh: D Lee, M Pyke, M Di Rollo, P Boston, H Southwell, B Laney, M Blair, G Anderson, D Hall, C Smith, A Kellock, S Murray, capt, A Strokosch, A Hogg, A MacDonald.
Replacements: A Kelly, A Dickinson, F Pringle, D Callam, R Lawson, P Godman, B MacDougall.
Referee: S Davey (RFU).