The first incident of note saw Gunners full-back Francisco Leonelli felled by a head-high tackle close to halfway.
The subsequent penalty allowed Edinburgh to pressurise the Ulster line but they failed to come away with any points.
To add to Edinburgh´s woes, Ulster proceeded to score from their first half-chance.
Stand-off David Humphreys snaffled a loose ball on the Edinburgh 10-metre line and seconds later left winger Andrew Maxwell was touching down.
Humphreys converted to put his side 7-0 ahead and then increased Ulster´s lead with a simple penalty matched two minutes later by a more difficult Duncan Hodge effort.
Simon Webster was then hauled down in the left-hand corner having been sent away after Phil Godman blocked a Humphreys kick.
The Edinburgh scrum was creaking but number eight Dave Callam managed to work the ball away and Rory Lawson won a penalty stroked home by Hodge.
Following a marvellous break from Ulster centre Andrew Trimble, Callam turned sinner with a professional foul.
He was sin-binned and Ulster heaved the short-handed Edinburgh scrum over their line for Issac Boss to score with Humphreys converting.
Four minutes from the interval Hodge was presented with a chance to narrow the gap with a penalty but the kick went wide and Ulster turned with a 17-6 lead.
Edinburgh made a lively start to the second half and a try seemed certain when Matt Mustchin took a quick tap in the Ulster 22, but Webster dropped the ball just a metre from the line.
Worse followed when Ulster, after nine minutes of the half, at last got up field to be awarded a penalty, goaled by Humphreys.
A third penalty by Hodge was immediately countered by Humphreys before Simon Best was sin-binned for stamping on Craig Smith.
From the penalty Edinburgh pressurised the Ulster line until awarded a penalty try converted by Hodge to cut the score to 23-16.
However, Ulster immediately countered with Maxwell´s second try.
In a crazy climax Maxwell then found himself in the bin, Humphreys kicked a penalty and Hodge closed proceedings with a try he converted himself.