Hogg's solo counter-attack followed Tim Visser's fifth try in seven internationals and Matt Scott's first as Scotland bounced back in style from their opening defeat by England.
Sean Lamont claimed another breakaway and Greig Laidlaw produced a perfect kicking display before Alessandro Zanni got a late consolation try.
The players who performed poorly in London emphatically made amends as Scotland took control of the game from the start and kept Italy out of their 22 for virtually the whole first half.
Scotland had the game wrapped up with two more tries within six minutes of the restart and produced a strong defensive display to keep out Italy for most of the second half despite the visitors dominating possession.
Scotland interim head coach Scott Johnson had only made two changes from the team that lost 38-18 at Twickenham, both of them enforced with hooker Ross Ford and flanker Robert Harley, making his first Scotland start, replacing the injured Dougie Hall and Alasdair Strokosch.
Italy came to Edinburgh on a high following victory over France and were looking for their fifth victory in seven Six Nations encounters with the Scots.
Last weekend's results had made Scotland odds-on favourites for a second consecutive wooden spoon but the hosts almost got off the mark inside two minutes when Laidlaw's measured kick initially fell perfectly into the path of Visser on the right wing. But the ball took an awkward bounce two metres from the line and drifted out of play as the Dutchman looked set to cross.
Luciano Orquera hit the post with a 38-metre penalty for Italy and Scotland stood up well to some pressure before the stand-off handed the hosts the chance to attack when he miscontrolled Hogg's kick.
Richie Gray spearheaded Scotland's resulting foray forward but some suspect handling gradually pushed the Scots back. However, hooker Leonardo Ghiraldini was penalised for an earlier infringement and Laidlaw kicked the opening points from about 30 metres.
Scotland were soon back in the Italian 22 but Ruaridh Jackson's crossfield kick failed to come off. However, South African referee Jaco Peyper pulled the Italians up for collapsing the maul seconds beforehand and Laidlaw kicked right in the middle of the posts from near the touchline to make it 6-0.
Scotland kept the pressure on and winger Giovanbattista Venditti gifted them a chance when he took a fresh-air kick. Ryan Grant picked up the ball and fed Scott to run down the left wing but scrum-half Tobias Botes produced a superb saving tackle from behind.
Italy could not get the ball far away though and Visser grabbed the first try in the 30th minute.
Jackson opened up the Italian defence following a scrum by feigning a pass on the left wing before feeding Visser, who cut inside one opponent and brushed off another before crossing.
Laidlaw converted and Scotland continued to keep the visitors out of their 22, but a scrum offence allowed Orquera to kick a penalty from almost 40 metres in the final minute of the half.
Scotland took just three minutes of the second half to wipe out that late blow. They switched play quickly following a lineout and Sean Maitland produced some penetrating play before releasing Scott, who ran clear from 30 metres out.
Laidlaw converted another tricky kick and Scotland went further ahead three minutes later when Hogg turned defence into attack in devastating fashion.
Andrea Masi broke into the Scotland 22 on the left flank and fed the ball inside to Orquera, who looked set to release Tommaso Benvenuti about 10 metres out.
But Hogg intercepted brilliantly and then sidestepped a challenge before sprinting forward. The full-back looked behind him as he crossed the halfway line and realised he was not going to be caught, and kept sprinting before throwing himself over the line for his third Scotland try in 12 appearances.
Laidlaw continued his excellent kicking display to make it 27-3 and some disciplined Scottish scrummaging repelled some Italian pressure before the hour.
Scott thought he had his second try on 65 minutes when he crossed in the corner following some patient build-up play but Maitland was adjudged to have given him a forward pass.
But Scotland had to wait just four minutes for their fourth following another breakaway.
Lamont won possession on the halfway line when he kicked the ball away from an opponent and ran clear to cross between the posts with Laidlaw completing the inevitable conversion.
Italy added some respectability to the scoreline in the 74th minute when they finally took advantage of a scrum, Sergio Parisse's reverse pass allowing Alessandro Zanni to cross.
Orquera's kick ensured Italy got into double figures but Scotland finished the game on the attack despite seeing replacement Geoff Cross yellow-carded in stoppage-time.