Norwich included summer signings Leroy Fer, Nathan Redmond and Ricky van Wolfswinkel in their starting lineup, while Kemy Agustien - who is expected to complete a move from Swansea City in the next few days - was included in the Brighton squad.
Van Wolfswinkel got his first sight of goal after nine minutes, but flashed his shot from 20 yards just wide of Tomasz Kuszczak's post.
Redmond, who arrived at Norwich from Birmingham City last month, had a big hand in the visitors' opener on 27 minutes.
The winger's cross from the right wing was met by Jonny Howson, who arrived late from midfield to put his side ahead.
Brighton took the game to Norwich in the second half, with March running at the heart of the defence. Ruddy had to dive low to his right to keep his side ahead.
Gary Hooper made his Canaries bow as he replaced Van Wolfswinkel on the hour mark, with Luciano Becchio also entering the fray.
March continued to cause problems, with Daniel Ayala denying the youngster with a good challenge, but there was no preventing the equaliser.
Brighton's Young Player of the Year 2013 cut in from the left wing before unleashing an unstoppable drive into the top corner of the net.
Luciano Becchio almost stole a late winner for Norwich, but his header dropped wide of the post.