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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1. Anthony Patterson - 6
Survived one scare in the second half when he couldn’t claim a corner, but distribution was good and composure generally impressive. 6
Photo: FRANK REID 2020
2. Carl Winchester - 8
There was more than a touch of fortune in his goal, his long-range effort deflected into the bottom corner. But it was a worthy reward for an excellent, composed display. Stepped out ever so well with the ball and was pretty much flawless defensively. 8
Photo: Frank Reid
3. Tom Flanagan - 7
Has had a very decent start to the season. Brings some important experience to the side and keeps it simple in possession when needed. Really composed. 7
Photo: JPI Media
4. Callum Doyle - 6
Good intent in possession, even if some of the end product was a little mixed. Defended strongly for the most part and deserves his first clean sheet of the campaign. 6
Photo: Getty Images