However, Ulster had all the early pressure and they had the hosts pinned in their own half until a break by Tania Rosser led to a penalty, which Jackie Sheils slotted between the posts.
Ulster's Laura Nichol came close to scoring but was pushed into touch just before the line.
Home scrum half Rosser continued to torment the Ulster back-line throughout the first half.
A scrum to Leinster five metres from the Ulster whitewash led to Leinster's first try of the match, which was scored by full-back Sheils.
The second half saw Leinster get over for a quick try. It was a well-worked score started by Louise Austin.
She picked off the back of the scrum and found Rosser who sniped over from close range.
Leinster spent the next 20 minutes camped in Ulster's 22. But the northern team's defence was too strong for Leinster who failed to score during that period.
Finally, Grace Davitt picked up on a loose ball in the visitors' 22 to get over for a try.
And Leinster then scored their fourth and final try in what was the last play of the match.
A great double tackle by team captain Coghlan and Julie Craig saw the ball being stolen by the ever alert Rosser who found space out wide to run in her second five-pointer.
* The Women's Interprovincial finals will take place next Saturday (October 25) at the Civil Service Sports Pavillion in Belfast.
The 3rd-4th place play-off between Ulster and Connacht will kick off at 12.30pm, while the final between Munster and Leinster will get underway at 2.30pm.