Connacht got precious little reward for a committed display, with Ian Keatley kicking a first half penalty and Eoin Griffin collecting a late consolation try.
In gaining ground in the Magners League's top-four, Leinster were clinical and second half touchdowns from Kearney, Fergus McFadden and Niall Morris powered them to victory.
Keatley kicked Connacht into a second minute lead, slamming a 49-metre penalty through the posts after Nathan Hines was seen going off his feet at a ruck.
Pinned back in their own half for most of the opening quarter, Leinster's early errors came as a result of intense pressure from the visitors.
Brett Wilkinson came close to breaching the try-line, following up on a clever move involving Keatley and Keith Matthews. But Leinster defended well and dotted down from their first serious attack.
Isa Nacewa missed a penalty from close to the ten-metre line, and from the very next phase of play, lovely hands from Hines, Shaun Berne and McFadden opened an avenue on the left for Kearney to blaze over in the corner.
Nacewa's missed conversion was followed by his first successful penalty, with Andrew Conway springing through a midfield gap in the build-up to it.
There was plenty of endeavour from both sides as the first half motored along, and Keatley missed a late chance to close the gap, drawing a 39-metre penalty to the right and wide.
Leinster opened the second half in better fashion, a close range penalty from Nacewa extending their lead to 11-3.
Connacht failed to turn a promising maul into a scoring chance and Leinster responded in decisive fashion, countering from deep with flair before Richardt Strauss' pass out of a tackle put Kearney over in the left corner.
Nacewa added the difficult conversion for a 15-point advantage, and Joe Schmidt's men were out of sight when McFadden plunged over on the right after replacement Morris had been held up short.
Then, with eight minutes remaining, Morris gathered McFadden's chip over the top and evaded Frank Murphy's attempted tackle to chalk up the bonus point.
Connacht had the final say, Dermot Murphy, Andrew Browne and Dylan Rogers stringing together the passes for Griffin to nip in at the corner for an unconverted score.
Speaking after the game, Leinster's captain for the night and man-of-the-match, Shane Jennings, said: "As expected, it was a tough game and they played deserve a lot of credit because they played well and had us under a lot of pressure.
"We got a bit more of the ball as the game went on and did a bit more damage, but Connacht were in charge for the first 20 minutes and we put ourselves under pressure.
"The Ospreys next week is another big challenge and every game is going to be tough as we bid to get into the top-four in the league.
"Thankfully it came good for us at the end, but there are a lot of frustrated heads in there (the dressing room), myself included."
|Leinster Rugby Score Card|
|Connacht Rugby Score Card|