Ireland led 21-0 after half an hour but yellow cards on either side of the break, for Ailis Egan and Claire Molloy, saw Italy claw back 10 points and press for more.
The match started ideally for Head coach Philip Doyle as Marie Louise Reilly crashed over.
And Ireland were soon on the scoreboard again, Kavanagh touching down in the 15th minute.
Neville then snapped up another try with Niamh Briggs adding the extras.
Egan’s yellow card came on 35 minutes and the visitors received a further boost just before the break when Cristna Molic careened over by the posts. Veronica Schiavon, guilty for two penalty misses, slotted the conversion to make it 21-7.
Ireland were on the back-foot in the second-half. Egan was back on less than two minutes when Molloy, excellent otherwise, was sent to the sin-bin.
Tondinelli landed a drop-goal in front of the posts but, press as they might, Italy could not force another score. Reilly, Laura Guest and Ashleigh Baxter were all commendable during the 20-minute spell of Italian supremacy.
It took a superb 50-metre break from winger Alison Miller to put the home side on the front foot. Her dart for the line came up only metres short but scrum-half Amy Davis picked up the loose ball to dive over and quell any fears of an Italian comeback.
With the away team wilting and the Ashbourne crowd in good voice, Kavanagh’s burst of pace left her markers on the wing trailing and scored in the corner. Jennifer Murphy came off the bench to replace Baxter and darted through a tiring Italy defence to dive under the posts. Grace Davitt landed the conversion to make it 40-10.
Ireland scorers: Tries: Niamh Kavanagh (2), Marie Louise Reilly, Amy Davis, Jennifer Murphy. Cons: Niamh Briggs (4), Grace Davitt (1).
Italy scorers: Try: Cristina Molic, Con: Veronica Schiavon, Drop-goal: Michela Tondinelli.
IRELAND: A Baxter (Ulster); N Kavanagh (Munster), N Briggs (Munster), G Davitt (Ulster), A Miller (Connacht); L Cantwell (Exile), A Davis (Leinster); F Coghlan (Leinster, capt), G Bourke (Munster), A Egan (Leinster); S Spence (Exile), M Louise Reilly (Leinster); L Guest (Munster), C Molloy (Exile), J Neville (Munster).
Replacements:P Fitzpatrick (Leinster), R O’Reilly (Connacht), S Fleming (Munster), H O’Brien (Munster), L Muldoon (Exile), N Caughey (Ulster), J Murphy (Exile)
ITALY: V Schiavon; M Furlan, M Sillari, P Zangirolami, M Diletta Veronese; M Tondinelli, S Barattin; E Chucchiella, S Zanon, L Gai; F Severin, C Molic; M Este, G Campanella, S Gaudino.
Replacements: D Ballarini, M Bettoni, A Trevisan, M Nespoli, V Chindamo, C Castellarin, S Stefan.