George North led the way with three tries in an astonishing performance by the visitors, although a last-gasp try by Leonardo Sarto for Italy made a potentially crucial dent in the Welsh points difference.
It was a complete contrast to the first half in which Italy at one stage led 13-11 with a spirited display while Wales looked nervous.
The Welsh victory left them on eight points and a scoring points difference of plus 53, leaving Ireland and England needing to win their games against Scotland and France by 20 and 16 points respectively to have a chance of lifting the trophy.
There was little hint of a Welsh onslaught in the first half with Italy showing a vast improvement from their lame performance in last Sunday's 29-0 defeat by France.
Kelly Haimona, who went off injured after only five minutes, and Luciano Orquera kicked penalties for Italy while Leigh Halfpenny converted two Wales penalties in a scrappy opening.
Centre Jamie Roberts scored the first Welsh try, winger Giovanbattista Venditti replied for Italy before Dan Biggar's penalty gave the Welsh a 14-13 halftime lead. In between, the prolific Halfpenny went off after suffering nasty blow to the head.
Both sides were unrecognisable after the break as the Welsh silenced the boisterous Italian support with a ruthless display of rugby.
Liam Williams opened the floodgates when he slipped through a gap in the Italian backline before a rampaging North scored a hat-trick of tries in 10 remarkable minutes.
Italy, meanwhile, lost their discipline as Andrea Masi and Quintin Geldenhuys were sent to the sin bin.
As the onslaught continued, scrumhalf Rhys Webb forced his way through half-hearted tackling for another try before captain Sam Warburton outpaced the Italian back line for their sixth try of the half.
Italy's performance was summed up when they spilled the ball in attack, Jonathan Davies surged clear and picked out Scott Williams who completed the Welsh scoring.
Biggar converted six conversions but there was a late twist when Sarto crossed for Italy following a surge down the left touchline, a try confirmed after a review which could prove crucial in the title race.
Sarto also scored a late try last year in a 52-11 defeat by England who went on to lose the title to Ireland on points difference on the final day of the tournament.
(Writing by Brian Homewood in Berne, editing by Ed Osmond)
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