Ross Stewart scored twice for the Black Cats after Bailey Wright’s headed opener to put the hosts in full control at the half-time interval.
Second-half goals from Luke O’Nien and substitute Leon Dajaku, his first for the club, then put even more gloss on the scoreline.
New signings Nathan Broadhead and Niall Huggins also impressed on their first starts for the club, as Johnson made five changes following Saturday’s 1-0 win over Bolton.
The result saw Sunderland move to the top of the League One table after nine games, as Wigan failed to beat Sheffield Wednesday at the DW Stadium.
Johnson will now hope his side can maintain momentum when they travel to Portsmouth on Saturday.
Our chief Sunderland writer Phil Smith has delivered his verdict on how each player performed against Cheltenham:
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1. Thorben Hoffmann - 7
Had virtually nothing to do in terms of protecting his goal, but his distribution was good and kept his side moving. 7 Photo: JPI Media
2. Carl Winchester - 9
Drove forward relentlessly and played a succession of superb passes into the channel. A big part of a tremendous attacking performance. 9 Photo: JPI Media
3. Tom Flanagan - 7
Had very little to do defensively in a dominant display, but passed the ball out with good intensity and precision. Strong again, and given a useful rest with an early withdrawal in the second half. 7 Photo: JPI Media
4. Bailey Wright - 8
Wasn’t tested much defensively but took his early goal well and most impressive was the way he took on Callum Doyle’s important role in playing out from the back and did it well. Important in the early momentum Sunderland built. 8 Photo: Frank Reid