Brazilian-born Thiago Motta scored the only goal of the game in just his second appearance for Italy since qualifying to represent the country.
And after all the pre-match talk of Italy's lack of quality and Slovenia's superior system in producing talented youngsters, it was the visitors who enjoyed much the better of things.
Even so, Italy coach Cesare Prandelli insisted that they still have a dearth of talent.
"It was a good game with two teams looking to play and to win," he said.
"Having won obviously we can say we were the better team but that doesn't change anything with regards the situation of the team.
"The fact that we were considered a second-rate team maybe gave the players a little extra motivation.
"We showed consistency in terms of matching the good performance we had against Germany (in a friendly last month).
"We have to stay on this track but we showed quality and the courage to try to play and win away."
In truth, Slovenia were a huge disappointment, hardly mustering a shot in anger on goal.
Their fans, a handful of which from rival teams Maribor and Olimpia Ljubljana fought amongst themselves before kick-off, seemed to have more fire in their bellies than the players.
Slovenia coach Matjaz Kek said the pre-match hype and expectation had got to his players.
"It was a very difficult match against team that held onto the ball well and our weaknesses were because we never had the ball," he said.
"There was too much expectation from the Slovenian public and probably the players paid for that.
"But at the end of the day, Italy were simply better."
And following Serbia's come-from-behind victory over Northern Ireland, unbeaten Italy are now six points clear at the top of Group C with half the qualification campaign behind them.
The first chance on seven minutes fell Italy's way as a half clearance dropped to Riccardo Montolivo 20 yards out but Samir Handanovic dived down low to his right to palm away the midfielder's volley.
The visitors went even closer halfway through the period as Giampaolo Pazzini hit a close-range shot on the turn from an angle that came off the outside of the post after a defensive mistake.
Slovenia's first decent chance in attack came shortly afterwards as captain Robert Koren tried his luck from 20 yards with a curler that Gianluigi Buffon, Italy's captain, palmed away with a diving save.
Handanovic was called into action on 35 minutes as he dived at Pazzini's feet to smother a chance and then got up to plunge at Antonio Cassano's dithering feet to block once again before Slovenia scrambled the ball clear.
Having bossed much of the first half, Italy started the better after the break as well with Stefano Mauri bursting forward to sting Handanovic's fingers with a low strike.
And the Udinese goalkeeper had to be alert to parry further efforts from Cassano and Alberto Aquilani as Italy looked to turn the screw.
Suddenly Slovenia exploded into life as Koren slipped in substitute Zlatan Ljubijankic whose shot from an angle Buffon tipped onto the bar.
Italy took the lead, perhaps deservedly, 17 minutes from time as the ball broke to Motta in the box and he slammed a deflected shot past an unsighted Handanovic.
Slovenia failed to put up much of a fightback, though, with Italy's most nervous moment coming from a dangerous in-swinging free-kick from Josip Ilicic that was headed behind for a corner.
Italy in charge of group after Slovenia victory
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