Luca Toni pulled one back and Tevez's fellow Argentine Juanito Gomez grabbed an equaliser for Verona in the fourth minute of stoppage time after coming on as a late substitute.
Juventus, who failed to win for only the fourth time in 23 Serie A games this season, stayed nine points clear of AS Roma, who were held to a goalless draw by neighbours Lazio.
Gervinho had a goal disallowed for Roma while Stefano Mauri came on at halftime for Lazio, his first match since completing a six-month ban for failing to report match-fixing in 2011.
Otherwise, there was little excitement in a disappointing derby with a surprising number of empty seats blighting the Stadio Olimpico.
Troubled Inter Milan produced their first win of the year when they beat lowly Sassuolo 1-0 with a Walter Samuel header at the San Siro, putting them level in fifth place with Verona.
Brazilian midfielder Hernandes made his Inter debut and midfielder Fredy Guarin his first appearance since his transfer to Juventus fell through in January.
Juventus, well on course to win a third successive scudetto, have 60 points, nine clear of Roma who are in their first season under French coach Rudi Garcia. Napoli, 3-1 winners over AC Milan on Saturday, are third with 47.
Tevez, whose performances have failed to impress Argentina coach Alejandro Sabella and who appears set to miss the World Cup, put Juventus in front in the fourth minute when he side-footed home from a rebound after Kwadwo Asamoah's shot was parried.
Juventus looked set to stroll home when Tevez calmly turned in Paul Pogba's incisive pass from a similar position inside the penalty area in the 21st minute, his 13th league goal of the season and one behind Serie A top scorer Giuseppe Rossi.
But promoted Verona had other ideas as Toni headed one back early in the second half, then saw a close range effort brilliantly stopped by Juventus goalkeeper Gianluigi Buffon.
In between, Juventus brought on Pablo Daniel Osvaldo, on loan from Southampton, for his debut and he made an immediate impact, hitting the post and having a goal disallowed.
Verona, who had two penalty appeals turned down, finally got a deserved equaliser when Gomez got in front of the Juventus defence to head in after a quickly-taken free kick.
Genoa and Sampdoria both scored early in 1-0 wins as they moved further away from the relegation zone.
Tenth-placed Genoa (30 points) moved above AC Milan when Luca Antonelli's early goal sank next-to-bottom Livorno.
Daniele Gastaldello's 11th minute header was enough for former Serbia coach Sinisa Mihajlovic's Sampdoria to overcome Cagliari, taking them up to twelfth.
Image: Carlos Tevez of Juventus celebrates
Photograph: Dino Panato/Getty Images
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