New Sunderland manager David Moyes watched his side edge Rotherham 2-1 in Saturday's pre-season friendly at New York Stadium.
Moyes, appointed as successor to new England boss Sam Allardyce this week, was in the stands to see goals from Fabio Borini and Charles N'Zogbia seal the victory, either side of a Jerry Yates strike.
Ronald Koeman, taking charge of Everton for the first time, enjoyed a 3-0 victory over Barnsley at Oakwell.
Kevin Mirallas' free-kick put them ahead before Gerard Deulofeu tapped home a second, and Ross Barkley belted in a fine strike to cap the win for Everton, for whom John Stones did not feature.
Jordon Ibe got his first Bournemouth goal in a 3-3 thriller against south-coast rivals Portsmouth.
The winger, a £15million ($26 million) signing from Liverpool, netted in the second half after a good solo run, though Adam May's 88th-minute equaliser denied his side the win.
Swansea City thrashed Bristol Rovers 5-1, meanwhile, with Andre Ayew, Leroy Fer, Stephen Kingsley, Kyle Naughton and Wayne Routledge all on the scoresheet in an impressive win for Francesco Guidolin's men.
Hull City began life after manager Steve Bruce's departure with a 2-0 win over Scunthorpe, while Burnley saw off Bradford 4-1, Andre Gray scoring twice as the Premier League side went 3-0 up in the space of five minutes in the first half.
Sofiane Feghouli scored one and set up another as West Ham beat Karlsruher 3-0, while Southampton defeated PEC Zwolle 4-0, Nathan Redmond scoring twice and Pierre-Emile Hojbjerg converting a late penalty.
Stoke City saw Jack Butland return after recovering injury but had to settle for a 1-1 draw with Preston North End, while Watford were held to a goalless draw by Anzhi Makhachkala.