An Antoine Sibierski strike just 43 seconds after his arrival as an 81st-minute substitute for Wigan was enough to condemn Derby to a seventh successive Premier League defeat at Pride Park.
They had the better of the chances in the first half, with their task seemingly made easier when Derby centre-back Claude Davis was dismissed for two bookable offences just before the hour.
Yet Wigan struggled against 10 men until Sibierski buried a 22-yard drive to end a personal five-month goal drought and give Wigan their first away league win of the season.
"When he [Sibierski] went off last week on a stretcher, I thought he was going to be out for two months," said Bruce.
"However, he had a go in training yesterday, confident there was nothing on the scans.
"That's the little break you need, that one of your big players like him was not seriously injured last week, and it was a great first touch in the end.
"To be fair we should have been out of sight in the first half because in the Premier League you don't get the chances like we had.
"When you miss those chances you think, 'Are we going to get punished?', but thankfully we didn't and the better team won."