Man-of-the-match Court was part of a dominant Ulster front row which earned a penalty try from a scrum, while Nick Williams and Andrew Trimble scored their other tries.
Fergus McFadden went over late on for Leinster but Court was delighted with the way his side had bounced back after last week's setback.
He said: "I think psychologically it's a massive boost for us. Last week we were all very disappointed with how we played. We got outplayed at home which was very disappointing so the boys were out to prove a point. Last time we played these guys was the Heineken final where they put a bit of a score on us.
"Other than playing for positions for the Irish team and things like that, it was a point to prove we can beat them. It's been a while since we have so it was good for the boys to get one back up and show we are genuine contenders this year, we just need to be more consistent.
"We've been ticking away quite nicely all year, maybe not as well last week as we would have hoped but the scrum's been our big strong point this year so we just wanted to keep it going and use it as a weapon."
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