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The Irish winger started on the bench – but was called on -along with Gordon D’Arcy on the hour and sparked Leinster to two quick tries.
David Holwell – in his first game for the province – had opened proceedings with a fifth minute penalty but Chris Paterson soon had the visitors on level terms – and they went ahead when Allan Jacobsen powered over for the games first try after only 15 minutes.
However the lead was short lived as Shane Byrne was bundled over from a lineout close in, with Holwell adding the conversion to give a 10-8 interval lead.
The New Zealander increased the lead with a second penalty but Edinburgh refused to be bowled over with Ali Hogg sending Rory Lawson in to equal the scores.
The game remained level until the introduction of Hickie and D’Arcy with the centre combining well with Shane Jennings to send Hickie in for his first, and moments later he had his second when D’Arcy and O’Driscoll created the opening for the winger to speed in.
Holwell converted, and added the extras to Aidan McCullen’s injury time score which secured the bonus point.
After the game Declan Kidney was pleased with the performance of his side. "They test your defence, they keep the ball alive very well and their ball retention is very good, so we’re delighted."
"There’s healthy competition for places at the moment," added Kidney. "Gordon and Denis are looking forward to getting their places; they showed good enthusiasm when they came on and that’s what we need".