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To add to Ulster's woes, lock Ryan Caldwell was red-carded for an off-the-ball stamp in the closing stages.
Edinburgh had the better of the jittery opening exchanges, and it was no surprise when they opened their account in the 16th minute.
A passage of patient play paved the way for centre John Houston to power through, with Phil Godman confidently adding the extras.
The hosts maintained the momentum but were held up by a combination of weak finishing and stout defence from the Ulstermen.
Edinburgh had luck on their side on the half-hour mark when they were the beneficiaries of a controversial penalty try.
Andy Turnbull was blocked a couple of metres short of the line by Scotland's Simon Danielli - and when the other visiting winger Mark McCrea also challenged, referee James Jones ruled the ball had been deliberately killed to prevent a score.
Ulster were justifiably furious as Godman slotted the formality of the conversion.
The visitors came more into the picture in the build-up to the break but could not turn pressure into points.
They broke their duck three minutes after the restart when Niall O'Connor kicked a penalty.
Edinburgh seized back the initiative with a kick-and-chase touchdown by Turnbull, endorsed by the video referee - and substitute Ally Warnock slotted the conversion to open up an 18-point gap.
Ulster refused to buckle, however - and a Mark Bartholomeusz try, converted by O'Connor, kept their hopes alive until Caldwell was dismissed.
There was still time for Warnock to clip over a penalty for Edinburgh to make sure.
Edinburgh 24 (14)
Tries: Houston, Turnbull 2
Cons: Godman 2, Warnock
Pen: Warnock
Ulster 10 (0)
Try: Bartholomeusz
Con: O'Connor
Pen: O'Connor
Edinburgh: De Luca, A. Turnbull, Cairns, Houston, Maxwell, Godman, Meyer, Allori, Kelly, G. Cross, Hamilton, Gissing, Mustchin, Rennie, S. Cross.
Replacements: Dey for Houston (72), Warnock for Godman (52), Lawrie for Kelly (60), Grant for G. Cross (55), Reid for Mustchin (14), Pringle for S. Cross (77). Not Used: Laidlaw.
Ulster: Cunningham, McCrea, Bowe, Mallon, Danielli, O'Connor, Campbell, J. Fitzpatrick, Brady, Court, Harrison, Caldwell, McCullough, Pollock, Wilson.
Replacements: Bartholomeusz for Cunningham (31), Larkin for O'Connor (75), Marshall for J. Fitzpatrick (54), Miles for Brady (70), D. Fitzpatrick for Court (60), Dawson for McCullough (52). Not Used: Barker.
Att: 3,468
Ref: James Jones (WRFU).





