The visitors took the lead midway through the first half when Dan Ballard was penalised for a foul on Sebastian Szymański, allowing Przemysław Frankowski to convert from the spot.
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Sunderland responded strongly, with Ballard and Reinildo both going close before the break.
Their pressure eventually paid off after the interval when Brian Brobbey capitalised on a loose header, using his strength to beat the goalkeeper and level the score.
The Black Cats completed the turnaround 10 minutes later. Enzo Le Fée’s free-kick caused problems in the box before Trai Hume fired home a superb half-volley.
Romaine Mundle later struck the post from a free-kick, but Sunderland held on.
The Lads now travel to Ipswich Town for their Premier League opener.