A workmanlike performance in Parma shot Leinster back to second place in the Pro12.
Matt O'Connor's men scored four tries in total, as they showed there is no shortage of talent coming through the ranks.
In the absence of several front-liners, it was the lesser known lights who took the limelight, most notably academy players Sam Coghlan Murray and Tadhg Furlong, who both looked comfortable in their elevated surroundings.
John Cooney, Noel Reid, Zane Kirchner and Darren Hudson all crossed for tries, and Jimmy Gopperth and Ian Madigan kicked the rest of Leinster's points between them.
For Zebre, Andries Van Schalkwyk scored the only try of the night on another disappointing night for the Italians.
They actually played all the smart rugby during the opening 15 minutes. Flanker Van Schalkwyk buried home from close range in that impressive period, but it only served to wake Leinster up, and they struck back with a try of their own seven minutes later through Cooney.
Gopperth added the conversion and a penalty on half-time.
In the second half, the visitors began to break Zebre down. Reid scored a cracking try 15 minutes in, Ian Madigan set up Kirchner for try number three, and two minutes from time, substitute Hudson got the bonus-point try.
Zebre – R Trevisan; G Toniolatti, R Quartaroli, K Ratuvou, D Odiete (D Berryman 55); K Haimona (G Bisegni 69) , A Chillon; M Aguero (capt) (A de March 66), T D'Apice (L Giovanchelli 66), D Chistolini (D Ryan 53); E Caffini (M van Vuren 44), G Biagi; F Ferrarini (C Filippo 31), A Van Schalkwyk (G Bernini 62), S Vunisa
Leinster – Z Kirchner; D Fanning, B Macken, N Reid, S Coghlan-Murray (D Hudson 72); J Gopperth (I Madigan 62), J Cooney (L McGrath 41); M Bent (J O'Connell 41, E Byrne 78), A Dundon (J Tracy 66) , T Furlong (M Bent 55); L Cullen, M McCarthy (T Denton 69); K McLaughlin (D Ryan 55), S Jennings, J Murphy.
Ref – N Hennessy (WRU)