The victory means that the reigning RaboDirect PRO12 champions are now only three points behind leaders and Irish rivals Munster.
And O'Connor admitted his side had certainly been made to work for their victory in Galway.
"Running down the hill with a slight breeze we were confident. We just had to look after the ball better, play in the right areas and back our execution," he said.
"They were always going to be very committed, they made us work for everything and it was good we held our bottle and got the result at the death."
Back-row Jordi Murphy claimed the man of the match award for the second game in a row for Leinster.
But the youngster refused to take any personal plaudits, instead insisting that the result was a team effort.
"I'm just happy to be getting a run of games under my belt," he said.
"I thought it was a one to 15 performance there and when the subs came on they did a great job as well - like Dominic Ryan's steal at the end was vital.
"He was just one of a number of players that came on and did a job for us, I just thought it was a great team effort overall."
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