The home side did not have it all their own way though with Paddy Jackson's boot seeing Ulster take and early lead before Leinster lost the influential Sean O'Brien to a shoulder injury.
But after heading in 10-6 up at the break, Murphy claims his side showed greater control over the contest in the second half.
"We went in at half time and we knew it was just one or two little things we had to tweak," he said.
"I thought we got better in the second half. I know we didn't score any tries, but I thought we were a bit more clinical overall.
"They were niggling at our ball a bit, winning penalties off us when we were deep in their 22, stuff like that. We just decided to put more pressure on, not leaving the rucks so bare, and we got what we wanted from it."
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up to our newsletter for regular updates on the RaboDirect PRO12
63x46.png){kind=logo}