It had all looked so different early on as Anthony Patterson produced an outstanding save to keep out Kieffer Moore's header from a pinpoint cross from Gustavo Hamer.
It came at great cost to Black Cats defender O'Nien, the veteran of over 300 games for the club, who had to be helped from the field with a dislocated shoulder after colliding with Moore.
The Blades were the better team, though, and that told in the opening goal as they broke decisively from a Sunderland corner.
Gustavo Hamer, the Championship's player of the year, led the charge and played a perfect to take out three defenders for Campbell to advance and lift the ball expertly over Patterson.
The Blades thought they had doubled their lead before half-time, as Burrows' first-time shot after Hamer's corner kick was cleared to him on the edge of the box found its way into the net.
But Sunderland were relieved when VAR, in place for the final, ruled that Patterson's view of Burrows' effort was impeded by Vinicius Souza, who was in an offside position.
Substitute Andre Brooks should have finished it for the Blades after 69 minutes when he broke inside the box following a mistake by Dennis Cirkin, but Patterson made a superb block.