Leinster picked up in the second half where they left off in the first when Prendergast picked up at the base of a ruck and darted over from a metre out to dot down, adding his third conversion of the game for 29-0.
The Bulls were controversially denied a try when Harold Vorster appeared to ground the ball, but after consultation with the television match official [TMO] referee Andrea Piardi ruled out the score.
It was the turn of Leinster to play with 14 men for 10 minutes when James Lowe received a yellow card for a deliberate knock-on infringement on his final appearance for the province.
Joe McCarthy executed an excellent turnover on the line to prevent a seemingly certain score, but soon after the hour mark the Bulls were not to be denied as they finally breached the holders’ defences as Moodie accepted an offload and stretched out to score, with Pollard adding the extras.
Any potential comeback hopes were ended, however, when Ruan Mortje barged over after the ball went quickly through the Bulls hands, but the referee adjudged Moodie had passed forward in the build-up after involving the TMO.
Replacement Byrne completed the scoring in the final minutes when he rumbled over between the sticks and converted his own try.
Leinster: Keenan; O’Brien, Ioane, Osborne, Lowe; Prendergast, Gibson-Park; Cahir, Kelleher, Furlong, McCarthy, Ryan, Deegan, Van der Flier, Doris (capt)
Replacements: Sheehan, Usanov, Clarkson, Mangan, Conan, McGrath, Byrne, Ringrose
Bulls: Le Roux; Arendse, Moodie, Vorster, Jacobs; Pollard, Papier; Steenekamp, Grobbelaar, Klopper, Vermaak, Nortje, Coetzee (capt), Louw, Hanekom
Replacements: van Staden, Wessels, Louw, Wiese, Rudolph, Burger, Gans, Carr