The sides scored a penalty apiece in the second period but Scott Johnson's men could not find any further breakthrough.
Wales had been boosted before the match as injury doubts Stephen Jones and Mark Jones both passed fitness tests and Shane Williams returned to the left wing after recovering from a dead leg.
Italy were forced into a late change when hooker Fabio Ongaro was replaced by Carlo Festuccia after going down with tonsillitis.
Flanker Mauro Bergamasco was also out injured, while Cristian Stoica dropped to the bench with Galon the starting full-back.
Italy, having been forced onto the back foot with clever tactical kicking from Stephen Jones and then Lee Byrne, were penalised in the first scrum of the match and Jones slotted Wales into a 3-0 lead after four minutes.
Wales lost scrum-half Dwayne Peel with a shoulder injury but it did not disrupt their early momentum and a silky backs move carved open the Italian defence for Mark Jones to score in the corner.
Hal Luscombe's inside pass to Williams, who had looped round off his wing, created the overlap for Jones to score his eighth try in 20 Tests. Stephen Jones missed the conversion and Italy's response was immediate as Galon scored.
The Azzurri had just had a score disallowed - winger Canavosio was ruled to have been in touch before off-loading - when Wales overthrew the lineout and Italy snatched possession back.
They spun the ball quickly wide for Galon to saunter untouched over the line.
But the full-back was too relaxed in touching down and under pressure from Luscombe appeared to have slid over the dead-ball line, but after the incident was referred to the television official Eric Darrier, the belated verdict was a try to Italy. Ramiro Pez missed the conversion.
Italy's defence remained under pressure and Stephen Jones found the breakthrough as he spun through tackles from Festuccia, scrum-half Paul Griffen and flanker Maurizio Zaffiri to score his sixth Test try and added the conversion.
Wales almost stung Italy with another score after 29 minutes when Luscombe hacked a loose ball out of his own half and bore down on the Italian try-line.
However, Bergamasco trailed him all the way and prevented the try. It was an effort typical of Italy's battling qualities and Pez, after missing with a 47-yard effort, opened his account from in front of the posts after Wales had been penalised for offside.
Wales were hammering away at the Italian line, forcing them into last-gasp defence as Matthew Watkins worked space for Robert Sidoli to gallop clear.
But that pressure was punctured two minutes before the interval when Canavosio picked off a pass Watkins had intended for Luscombe and sprinted 70 metres for the try. Pez's conversion levelled the half-time score.
Pez missed the opportunity to kick Italy ahead just two minutes into the second half.
Bergamasco, one of Italy's star men this championship, launched a blistering counter-attack and chipped into space behind Byrne only for the Wales full-back to tackle him off the ball.
Byrne escaped the yellow card but this time Pez was successful with the penalty and Italy moved ahead.
The Azzurri had begun the second half with real purpose and Wales lost their composure.
Italy had to make their pressure count but Pez missed with another penalty attempt and Stoica, on for Canavosio, sent a drop-goal effort wide.
Wales were ringing the changes, with flanker Alix Popham and prop Gethin Jenkins both introduced before the hour.
Jones levelled the scores again at 18-18 with a long-range penalty, but Wales were having to work hard for both possession and territory and could not eke out any further points.