Wales' usual skipper Alun Wyn Jones came off the bench after 50 minutes and helped lift the side with his imposing on-field presence.
Italy made the scoreline more respectable when Allan exploited a gap and teed up Edoardo Padovani into the right corner. Reps: L Bigi, C Traore, T Pasquali, F Ruzza, M Barbini, E Gori, I McKinley, T Benvenuti.
Elsewhere, centre Owen Watkin, flyhalf Dan Biggar, lock Jake Ball and hooker Elliot Dee are all included, with Navidi moving from blindside flank to No 8. Reps: R Elias, W Jones, D Lewis, AW Jones, R Moriarty, G Davies, G Anscombe, H Amos.
Gatland said: "We have made a number of changes this weekend, but have picked what we think is a very exciting team that still has huge experience throughout it".
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"If that was a normal year, on reflection, maybe we wouldn't have made so many changes. We wanted to give everyone in the 31 (man squad) an opportunity to be involved in the first two games". "It should be a tasty one", Davies, captaining the side for the first time on his 70th appearance, told ITV Sport. He has a huge amount of experience, is a great leader and it is a great honour for him to lead his country.
But Gatland warned: "Italy will be hurting after last weekend, but they are a different proposition in Rome".
Follow live updates as Italy host Wales in the Six Nations. They triumphed 23-20 in 2007 and 30-22 in 2003.
He was already being asked by rugby writers if it was time to re-embrace Italy's traditionally defensive style of play, based around the scrum, which left less room for errors and occasionally earned the Azzurri a win.
Eddie Jones talks up 'greatest Welsh side ever'
France coach Jacques Brunel admitted it had been no contest and that England had beaten them up from the start. Come and referee a game yourself then you can let us all judge you then.
Ireland captain Rory Best praised the strong performance of Carbery, who replaced Sexton and played an influential role during the second half after throwing the intercepted pass that led to the only Scottish try.
But, seven months out from the World Cup in Japan, Gatland was satisfied to be heading back to Cardiff - and a date with England in a fortnight - with two wins in the bag.
Wales' 26-15 victory equalled the longest unbeaten run in their 138-year Test match history, making it 11 successive victories and matching the sequence set between 1907 and 1910. Their late comeback against Scotland at Murrayfield last Saturday could not mask another below-par Six Nations display under Conor O'Shea, who has yet to register a win in the tournament since taking over in 2016.
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