In the first Tees-Wear derby in over a year, Riley McGree scored the only goal.
McGree scored after O'Nien's last-ditch tackle hit his foot.
The hosts missed a number of chances to extend their lead in the game.
The win lifted them to 14th in the Championship.
Chris Wilder's team had a poor start to the season and only won one of their first seven games.
Alex Pritchard should have opened the scoring for the Wearsiders after seven minutes but they were held to a 2-2 draw.
McGree's volley bounced over the bar and his strike was saved by the Black Cats keeper in the first half.
He scored the second of his three chances at the end of the first-half to give his team a lead they wouldn't relinquish.
The team had the upper hand in the second half and had a chance to double their advantage.
It has been 14 years since the last game between the two teams.
It was the first defeat for the Black Cats' manager, who grew up in the city and captained the club.
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