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Wales, who beat France in their opening match, dominated possession but scored only two tries in a performance unlikely cause many concerns for their next opponents, England.
The visitors took 54 minutes to score their first try, when winger Josh Adams touched down, having shown too much respect to the home side in the first half when starting flyhalf Dan Biggar kicked four penalties.
"If we play like that against England, it could be embarrassing," Wales head coach Warren Gatland told ITV Sport, barely savouring the fact he had just steered the team to equal a Welsh record that was set from 1907-10.
"But we won't play like that," he added. "There are lots of things we need to improve on for England."
Centre Jonathan Davies, who captained Wales for the first time, also seemed annoyed.
"I think there was a lot of frustration," Davies said, remarking that Wales had failed to generate enough points despite dominating territory and Italy giving up 11 penalties, almost twice the number handed to the visitors.
Gatland had made 10 changes from the side that came from 16 points behind to beat France in Paris, bringing back Dan Biggar as flyhalf in place of Gareth Anscombe and teaming him with a new scrumhalf in Aled Davies.
Lack of precision
Biggar played well with ball in hand but lacked precision when kicking for field position and he was replaced by the more accurate Anscombe early in the second half.
Despite Wales dominating territory and possession for the first 30 minutes, it was Italy who scored the first try.
South African-born flanker Brahm Steyn barged across the line close to halftime, breathing hope into the perennial wooden-spooners who have now lost 19 straight Six Nations matches stretching back to 2015, a record for the tournament.
The long-suffering Rome crowd also came alive, but Italy continued to concede too many penalties, squandering possession and momentum.
In the second half, both sides threatened, each scoring a try in the final 10 minutes -- through Wales centre Owen Watkin and Italy winger Edoardo Padovani -- but the result never looked seriously in doubt.
Italy coach Conor O'Shea, who ushered in a new brand of attacking rugby when he took over in 2016, could come under growing pressure to reconsider his tactics.
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.
Italy captain Sergio Parisse gave O'Shea his backing, reaffirming his confidence in the Irish coach's gameplan despite another loss.
"This is a very young squad with lots of talent. It has a big future and I am always confident," Parisse said. "It's always difficult after a defeat... but as a captain I must always be positive and hold my head high."