The hosts enjoyed an excellent first 20 minutes, but were rewarded with just 7 points when it could have been more. A solid scrum gave the Ulster backs front foot ball and they fully exploited - Sean O’Hagan found Conor McKee who broke the line before providing the scoring pass to centre partner Sam Arnold. O’Hagan added the extras with a well struck kick.
Arnold almost scored again moments later when O’Hagan made an incisive break but after drawing the fullback, his pass was just behind his supporting team mate.
Leinster responded when right wing Adam Leavy touched down after great work by outhalf Joseph Carberry, who landed the difficult conversion to draw level.
O’Hagan’s penalty gave Ulster a 10-7 lead at half time but Carberry cancelled it out with an effort of his own early in the second half.
Arnold grabbed his second with 15 minutes to play after superb work by his forwards. Some big carries, particularly from captain Michael Lagan and second row Nigel Simpson, punched holes in the Leinster defence and Arnold was on hand to crash over the whitewash from a couple of metres out. Jack Milligan - on the field after replacing O’Hagan - saw his conversion attempt rebound off the post.
The visitors pushed for a late match-winning score but Ulster defended resolutely to hold them out and seal the win.
They will now travel to Cork next Saturday in a bid to beat Munster and become inter-provincial champions.