The striker scored the only goal of the game and missed a second half penalty as Massimiliano Allegri's side recorded a narrow win on Sunday
The Argentine, who notched a double to help dump Borussia Dortmund out of the Champions League in midweek, lit up the contest with a brilliant solo goal after 25 minutes.
It was not a flawless performance from the former Manchester City man, who saw a second-half penalty saved, but a third consecutive league win and a 17-point lead at the summit rarely appeared to be in doubt.
Roma, currently on a dismal run of form in second place, can close that substantial gap when they face Cesena on Sunday.
A slack pass from Leonardo Bonucci presented Niang with the opportunity to give Genoa a second-minute lead, but the forward curled narrowly wide from 20 yards.
Neither defence looked particularly assured during the opening exchanges and Facundo Roncaglia made a last-ditch block to deny Juventus striker Fernando Llorente.
Genoa felt they should have had a penalty in the 14th minute, but Diego Perotti was booked for simulation following a challenge from Claudio Marchisio.
Juventus continued to struggle for fluency but a moment of magic from Tevez put them ahead.
The Argentina forward slipped past a pair of defenders on a typically bustling run before firing home an angled shot via the underside of the crossbar for his 16th Serie goal of the season.
The visitors' early verve disappeared and it was almost 2-0 on the stroke of half-time as Giorgio Chiellini struck the crossbar when Genoa failed to fully clear a corner.
Mattia Perin was injured in the build-up to the Chiellini chance and was replaced by understudy Eugenio Lamanna soon after.
And, as he did after emerging from the bench against Roma in December, Lamanna thwarted the opposition from the penalty spot.
Roncaglia was penalised for a trip on Roberto Pereyra but Tevez failed to convert his 62nd minute spot kick as the keeper produced a diving save to keep his side in the game.
Genoa's best chance for a leveller came 10 minutes from time, as Andrea Barzagli cleared brilliantly to deny Perotti at the far post, but they could not find a way through, with Juventus continuing their march towards the title.