Edinburgh had tested the home defence to the full for the opening quarter, but Ulster began to use their possession wisely and a David Pollock try, converted by Clinton Schifcofske on 26 minutes gave them a 7-0 lead.
Join Richard Mulligan for his personal views on YOUR RUGBY hereApart from that conversion, Schifcofske's poor kicking streak continued missing penalty attempts on 20 and 40 minutes, while just after the break two kicks inside six minutes from David Blair brought Edinburgh right back in at 7-6.
Schifcofske did kick two penalties, having missed another, which did restore the seven point lead, only for a silly penalty against giving replacement Phil Godman an easy three-pointer and there were just four in it again.
But Ulster were to hold out this time and a crucial turnover in injury time as Edinburgh were pressing gave the Irish Province that much sought after first win.
Ulster: B Cunningham; C Schifcofske, D Cave, P Steinmetz, A Trimble; N O'Connor, C Willis; T Court, R Best, (capt), BJ Botha, E O'Donoghue, R Caldwell, S Ferris, D Pollock, R Diack.
Replacements: N Brady, J Fitzpatrick (Court 60), C Del Fava (O'Donoghue 60), M McCullough (Ferris 74), I Boss (Willis 44), I Humphreys, T Nagusa.
Scorers
Tries: Pollock
Pens: Schifcofske (2)
Cons: Schifcofske
Edinburgh: J Thompson; J Houston, H Southwell, N De Luca, M Robertson; D Blair, M Blair (capt), A Jacobsen, A Kelly, G Kerr, J Hamilton, B Gissing, M Mustchin, A Hogg, S Newlands.
Replacements: R Ford (Kelly 40), G Cross (Kerr 40), C Hamilton (Gissing 50), C Fusaro, G Laidlaw (M Blair 69), P Godman (D Blair 50), C MacRae (Thompson 64).
Scorers
Pens: D Blair (2), Godman
Ref: Carlo Dimasco (Italy)
Man of Match: S Ferris
Att: 8,148
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