Giaccherini, Vucinic and Asamoah all hit after the interval to pull the Bianconeri back from one goal down, extending their unbeaten run to 42 games in the process
Ciro Immobile had fired the home team into an early lead, but Emanuele Giaccherini's finish followed by a penalty from Mirko Vucinic ensured that the Old Lady would take all three points from the Stadio Communale.
Kwadwo Asamoah then put the result beyond any doubt with a close-range finish, consigning Genoa to defeat in a game when victory appeared within their grasp.
While Juventus dominated possession in the early exchanges, but it was the swift, direct attacking of the home side that yielded the best opportunities.
In fact, Genoa could have netted twice in the opening 10 minutes. Marco Borriello fashioned a golden chance one-on-one with Gianluigi Buffon after latching on to a long ball that eluded everyone in the Juve defence, but dragged his shot just wide of the left post.
Immobile was the next man to go close, and the young star co-owned by Juventus really should have punished the Bianconeri on the break. The striker was left alone on the counter to bear down on Buffon after running almost 40 metres, but under pressure from Barzagli fumbled his effort and failed to force a save from the veteran goalkeeper. He would soon make amends, however.
A swift one-two with Andrea Bertolacci left Immobile clean through in the area, and this time he would not let Juve off the hook, with a low drive leaving Buffon no chance on its way to rest in the bottom corner.
The visitors had looked toothless throughout the opening period, and almost went two down when Borriello, clean through after expertly turning Chiellini, was denied by the veteran keeper from point-blank range.
With one of their few opportunities in the entire half, the Old Lady almost hit back. Alessandro Matri took hold of a wonderful through ball from Emanuele Giaccherini and had the goal at his mercy; but to the chagrin of the visiting support, the striker could only scoop his shot harmlessly over the bar.
It was a rare opening for the Serie A holders who, despite enjoying ample time on the ball, showed little threat in the final third against a team always looking to do damage on the break.
Although the Turin side came out after the interval determined to peg their rivals back, it was again Genoa who continued creating chances. Mario Sampirisi thought for a second he had doubled the advantage after meeting Bosko Jankovic's perfectly-placed free kick, but the header only found the side-netting.
Sebastian Giovinco then had the Rossoblu reeling when he cut in from the left, striking against the post before Giaccherini just failed to turn home the rebound. The midfielder was amongst Juve's most dangerous men, and hit just wide with a spectacular volley as pressure mounted on the home team.
At the other end Jankovic also struck the woodwork, denied by the bar as he looked to extend the lead in a game that was becoming more open by the minute. Bertolacci then was guilty of squandering an excellent chance to add a second, and punishment was swift as Juve immediately hit back.
On the counter directly from the Genoa man's miss, the ball was worked to Giaccherini who had crafted space on the edge of the area. Having narrowly missed the target before, this time the midfielder made no mistake as he drove past Sebastien Frey and kept alive Juventus hopes of further extending their outstanding unbeaten run.
The goal put an end somewhat to the manic action of the second half's opening minutes, with both teams settling into a more fluid rhythm. With just 15 minutes remaining, however, Juve were handed a golden chance to take the lead. Sampirisi conceded a penalty when he clumsily felled Kwadwo Asamoah in the box, and Mirko Vucinic made no mistake from the spot to make it 2-1.
The killer blow for the home team arrived seven minutes from the end. A cross from the right was deflected across the goalmouth, and Asamoah was on hand to turn the ball in unopposed and ensure that the visitors would be celebrating on Sunday.
The win means that Juventus maintain their 100 per cent record in the 2012-13 season, also recording their 42nd consecutive game without losing in Serie A. The Turin side keep pace with Lazio and Napoli as the only teams to have won all three fixtures so far.