Juve's third straight victory by the same scoreline put them on 67 points as they remain 14 points clear of second-placed AS Roma, who also won 1-0 at lowly Cesena, with 10 games left.
Despite the size of their lead, Juve coach Massimiliano Allegri remained cautious, telling Sky Sport Italia: "We haven't won anything yet. We'll celebrate when the time comes."
Tevez scored when he collected a pass from Claudio Marchisio on the edge of the area in the 25th minute and ran past Andrea Bertolacci and Sebastien De Maio before rifling a shot past Mattia Perin from an acute angle that went in off the bar.
The Argentine, the league's top scorer with 16 goals, then missed a penalty just past the hour mark when Genoa's substitute keeper Eugenio Lamanna, who had replaced the injured Perin nine minutes earlier, made a terrific save.
Daniele De Rossi's first-half strike from close range gave struggling Roma their first win in five games at Cesena.
"Today there was a battle to be won. We have ten (games) left awaiting us," Roma midfielder Radja Nainggolan told reporters.
De Rossi, filling in as captain for the injured Francesco Totti, took advantage of Jose Holebas's low cross in the 41st minute to score his second goal of the season.
LAZIO WIN
Lazio remain one point behind Roma after a 2-0 win at home to Verona. A Felipe Anderson header and a powerful Antonio Candreva free kick handed Lazio a sixth straight victory.
Sampdoria stayed in the hunt for a spot in next season's Europa League after defeating visitors Inter Milan 1-0 with a ferocious free kick by Eder that went in off the post.
Sinisa Mihajlovic's side are fourth on 48 points, one above Napoli who scored a last-gasp goal to salvage a 1-1 draw at home to relegation-threatened Atalanta, who had Alejandro Gomez sent off after he received a second yellow card.
The home side, despite playing for 35 minutes with an extra man, fell behind in the 72nd when Mauricio Pinilla took advantage of an Henrique blunder. Napoli substitute Duvan Zapata headed in the equaliser one minute from time.
Sixth-placed Fiorentina drew 2-2 with Udinese thanks to Mario Gomez's second-half double and they now have 46 points.
Bottom side Parma, declared bankrupt last week, went down 2-0 at home to Torino with their 20th defeat in 26 games after captain Alessandro Lucarelli was sent off in the 36th minute.
Empoli's Riccardo Saponara struck a second-half double as they defeated Sassuolo 3-1 in a mid-table clash.
(Editing by Ken Ferris)
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