Chris Hughton's side went ahead through Jonny Howson and despite Brighton playing well, it did not look like the Championship club would be able to cancel out the 25-year-old's effort.
However, with just seven minutes left, Solly March scored with a stunning shot from 25 yards to share the spoils between the two sides.
Following a tough tour of America, which saw the Premier League side lose both friendlies to the Portland Timbers and San Jose Earthquakes, Hughton opted to start three of his new signings.
Leroy Fer, Ricky van Wolfswinkel and Nathan Redmond were all in the starting XI and the latter impressed from the off.
It was Javier Garrido who set up Howson's opener after 27 minutes with his cross inviting a goalmouth scramble that the former Leeds United captain seemed to get the last touch to.
Hughton's side had a narrow advantage that luckily remained as Brighton's Andrea Orlandi slipped in front of goal just a few yards out to miss a sitter.
New Norwich signing Gary Hooper entered the fray in the second half, but was unable to make an impact, along with fellow substitutes Luciano Becchio, Jacob Butterfield and David Fox.
And March punished Norwich with seven minutes left as the 19-year-old midfielder smashed a long-distance shot past John Ruddy.
Hughton's side will next face Sporting Braga away on Friday before pitting themselves against La Liga club Real Sociedad four days later.
