Bournochans goalkeeper James Ward-Prowse made the most of his chance to open the scoring after just three minutes as Sunderland were held to a goalless draw at the Stadium of Light.
James Ward-Potter was booked by the referee for his challenge on Daniel Sturridge on the edge of the box as Sunderland went ahead.
After a couple of minutes of added time, Sunderland had a second chance to equalise when striker Chris Brunt’s pass was deflected to Ward-Spencer.
The former Blackburn and Stoke City man did well to turn the ball into the top corner but it was only half-time and Sunderland held on for a 1-0 victory.
James McCarthy scored his third goal of the season for Sunderland, who are now three points clear at the top of the table.
The Sunderland goalkeeper made the right call to give his side a second goal after the break, but it could not be ruled out by referee Mike Dean.
Bournemouth are now nine points behind leaders Leicester City and are also six points adrift of fourth-placed Arsenal.