Middlesbrough won the 145th Wear-Tees derby 1-2, thanks to a first-half brace from Uruguayan Cristhian Stuani.
Cristhian Stuani handed Aitor Karanka his first Premier League victory as Middlesbrough claimed the Wear-Tees derby honours at Sunderland.
Chelsea came from a goal down at Watford on Saturday to make it two wins from two Premier League games for Conte.
English Premier League: Patrick Van Aanholt (71'), Sunderland 1-2 Middlesbrough
English Premier League: Brad Guzan (60'), Sunderland 0-2 Middlesbrough
A match heading for disaster turned into a very good Everton win due to an early tactical intervention by Ronald Koeman.