David Humphreys kicked all of the Ulster points
Edinburgh (17) 20
Pens: Paterson (4)
Drop goal: Godman
Ulster (9) 15
Pens: Humphreys (5)
Ulster lost for the first time this season as Edinburgh emerged five-point winners at Murrayfield on Friday night.
The Scottish side led 17-9 at the break with Ben Cairns scoring a late try to add to three penalties from Chris Paterson and a Phil Godman drop goal.
David Humphreys kicked three penalties to keep the Irish province in touch.
The former Ireland fly-half added two more second-half penalties, but another Paterson effort ensured victory for his side while Ulster took a bonus point.
Ulster dominated early on and a Humphreys penalty gave them the early advantage.
Godman replied with a drop goal on eight minutes and Paterson kicked two penalties to give the Gunners a six-point lead.
Humphreys replied with another two penalties and Paterson responded with one before Cairns went over the line to extend Edinburgh's lead to eight points.
Ally Hogg surged up the field, Dougie Hall and Matt Mustchin provided the link and Cairns shook off two challenges before surging into the corner.
Humphreys began the second half by kicking a penalty and then missing with another effort before making amends to reduce his side's arrears to 17-15.
Paterson's fourth penalty of the game gave the Gunners a deserved win.
Ulster coach Mark McCall:
"We are very disappointed with the result and our performance.
"There was not much shape to our play in the first half and although we improved a bit in the second half we were second best to Edinburgh in this one.
"We made crucial mistakes at vital times, gave away soft penalties and had no killer touch while Edinburgh played well and defended strongly.
"We deserved to lose as we were not good enough in this game but we have a big game at home to the Ospreys next week and we will look for a reaction in that game."
Edinburgh Gunners: H Southwell; C Paterson (capt), M Di Rollo, R Dewey, B Cairns; P Godman, M Blair; A Jacobsen, D Hall, A Dickinson, M Mustchin, S Murray, A Strokosch, R Rennie, A Hogg.
Replacements: A Kelly, D Hewett, F Pringle, D Callam, G Laidlaw, D Hodge, M Pyke.
Ulster: B Cunningham, M Bartholemeusz, P Steinmetz, P Wallace, A Maxwell, D Humphreys, I Boss; J Fitzpatrick, R Best (capt), B Young, M McCullough, T Barker, S Ferris, K Dawson, R Wilson.
Replacements: P Shields, T Court, L Stevenson, N McMillan, K Campbell, K Maggs, S Young.