Carl Winchester scored the only goal of the game after his deflected effort in the 64th minute left Wimbledon goalkeeper Nik Tianez rooted to the spot.
Johnson made one change to his starting XI following the Black Cats’ 1-0 defeat at Burton, with Alex Pritchard coming into the side to make his first league start for the Wearsiders.
The playmaker replaced left-back Dennis Cirkin in the starting XI, with Dan Neil moving back to full-back and Elliot Embleton dropping into a deeper midfield role.
A third league win of the season means Sunderland have taken nine points from their first four fixtures.
Our chief Sunderland writer Phil Smith has delivered his verdict on how each player fared at the Stadium of Light:
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The playmaker replaced left-back Dennis Cirkin in the starting XI, with Dan Neil moving back to full-back and Elliot Embleton dropping into a deeper midfield role.