Norwich created the better chances in a poor first half with Nathan Redmond and Gary Hooper calling keeper Vito Mannone into action, and the Black Cats offering little of note until Phil Bardsley tested John Ruddy with a long-range 37th-minute effort.
However, Sunderland rallied after the break with Brown heading against the outside of an upright, although substitute Ricky van Wolfswinkel should have put the visitors ahead eight minutes from time, only to be denied by Mannone.
Opposite number Ruddy almost handed the Black Cats victory seconds later when he raced from his line in a vain attempt to beat Fabio Borini to the ball, but when the Italian squared for Ki Sung-yueng, the South Korea international fired over the unguarded goal.
The Black Cats, fortunes took a further turn for the worse when defender Brown was sent off in stoppage time after he clattered into Van Wolfswinkel close to the sideline.
Hughton said: "The challenge was certainly reckless, there's no doubt about that.
"It's a shame because it was a whole-hearted game, both teams ended up having a real go. At one stage, it was pretty end-to-end and it was a shame, really, because it wasn't that type of game.
"They have had a good week, Sunderland, and that can really buoy a team.
"Irrespective of any difficulties they have had, they have still got very good players, so in this day and age any draw, particularly with a clean sheet, away from home, that's a good draw."