Wales also came a cropper four years later at the Stadio Flaminio in their 23-20 defeat and only a late Tom Shanklin try spared them a similar fate in 2009.
On that occasion Gatland nearly paid the price for resting several key players, and Owen is adamant another upset will be on the cards unless Italy are treated with total respect.
He said: "They key is they put Italy to bed early on; the longer they are in the game the more dangerous they will become like Ireland found.
"I think the England result actually makes it more difficult for Wales as Italy will be desperate to bounce back with a good performance.
"They have some excellent players right through their team and in Martin Castrogiovanni and Sergio Parisse have two of the best players in their position in the world.
"When they get the crowd behind them it is a terrific atmosphere so it is very important Wales start with a bang.
"The Wales defence was excellent against Scotland and it will need to be the same in Rome.
"The one thing that works in Wales' favour is that I just can't see Italy scoring enough points to win outright."
The 2003 defeat was only Italy's second ever Six Nations victory - the other coming against Scotland in 2000.
It marked a low period in Welsh rugby in which they lost 11 consecutive matches and finished with Wooden Spoon.
But it was the defeat to Italy, according to Owen, which was the bitterest pill to swallow.
He said: "I played in 2003 and they made it a really difficult game for us especially around the contact area.
"Italy were deserved winners but Wales were not in a good place back then. There was a lot of uncertainty surrounding the team.
"We were turned over far too easily and the more doubts that started to spring up, the worse we played.
"I remember the feeling in the dressing room afterwards and it was horrible.
"No one wanted to be part of the first Wales team to lose to them in the Six Nations and it took several weeks for that feeling to disappear."