The Bianconeri finished fourth last season, thanks largely to the contribution of the Chile winger, but his departure to Barcelona raised question marks over whether they could repeat the trick this time around.
Early goals from Dusan Basta and the impressive Antonio Di Natale settled any nerves, though, while the performance of Gabriel Torje suggested Sanchez may not be as irreplacable as first thought.
A summer arrival from Dinamo Bucuresti, the 21-year-old Romania international was involved in almost everything Francesco Guidolin's men did.
However he was allowed to shine by a pedestrian Lecce side who found themselves a goal down inside the opening two minutes.
Giovanni Pasquale's low cross was not dealt with and reached Basta, who did the rest from close range to give Udinese a dream start.
David Di Michele took aim from range in a bid to level things but was some way off and, before the 16th minute was up, his side were two goals down.
Basta started the move as he played in Torje, whose shot fell into the path of Di Natale and he displayed his finishing prowess from just inside the area.
Full of confidence, the Udine side looked for a third and Julio Sergio had to fling himself at Di Natale's drive, before Lecce threatened again, with Guillermo Giacomazzi's header forcing Samir Handanovic into a save six minutes before the break.
Sergio made a regulation stop from Danilo after the restart, Kwadwo Asamoah hit wide and Torje drilled over as Udinese continued to pour forward, before Andrea Bertolacci tried to mount a late Lecce fightback with a shot from distance.
He was unable to inspire anything, though, with Edward Ofere the other home player to attempt a token effort on goal as Udinese eased home.