After a runaway title win in 2013-14, Juve are strongly fancied to make it four Scudetti in a row at the end of the campaign, and Saturday's result at Juventus Stadium means the Massimiliano Allegri era has begun in positive fashion.
In his first competitive home match in charge, Allegri had to contend with the absences of key men Andrea Pirlo, Giorgio Chiellini and Arturo Vidal, but the home side had little trouble in overcoming an Udinese side that lacked any potency, even with the prolific Antonio Di Natale in attack.
Di Natale came into the clash having scored seven goals in two matches this season, but the 36-year-old had little effect on the affair as an early strike from Tevez was added to by Marchisio's effort from distance 15 minutes from time.
Juventus had chances to add to their margin of victory, while the closest the visitors came to a goal saw Igor Bubnjic's close-range effort ruled out for offside midway through the second half.
The result means Juve have now won all of the past six meetings between the two sides, and the defending champions extended their winning sequence at home in the league to 20 games in the process.
Allegri made three changes from the side that defeated Chievo 1-0 on the opening weekend.
Fernando Llorente was selected to partner Tevez in attack, while there was a competitive Juve debut for Patrice Evra and on-loan midfielder Roberto Pereyra made his first start, against his parent club.
The hosts were ahead in the eighth minute when Tevez swept home Stephan Lichtsteiner's cut-back from the byline after the Switzerland international had combined well with Pereyra down the right-hand side.
Pereyra wasted a chance to net against his former employees in the 29th minute, firing over the crossbar from just inside the area after being teed up by Llorente.
Tevez blasted over four minutes later as Juve continued to dominate, while Lichtsteiner and Paul Pogba both spurned presentable opportunities with weak efforts as the half drew to a close.
Pogba tested goalkeeper Orestis Karnezis with a curling free-kick four minutes after the interval, and Martin Caceres was just unable to connect with Tevez's inviting free-kick at the back post.
Bubnjic thought he had levelled in the 67th minute when he tapped home from six yards, but the referee's assistant raised his flag with replays showing the Croat to have strayed marginally beyond the last defender.
Tevez brought another save out of Karnezis four minutes later as Juve went in search of a second, which duly arrived when Marchisio thumped a low shot into the bottom right-hand corner from 20 yards.
A further boost for Allegri came late on as close-season arrival from Real Madrid, Alvaro Morata, emerged as an 89th-minute substitute for his debut having recovered from a knee injury, the Spaniard forcing a good save out of Karnezis in his brief cameo.