The former Celtic striker netted a quick-fire double early on, but the Portuguese side levelled in the second half through Paulo Vinicus and Rafa at the AXA Stadium
Hooper - who joined Norwich from Celtic last month - looked sharp from the outset at the AXA Stadium and grabbed an early double to put the Premier League side in command.
However, Braga came back strongly after half time to claim a well earned draw thanks to strikes from Paulo Vinicius and Rafa.
Chris Hughton's side started the match on the front foot and thought they had taken the lead after just six minutes, but Wes Hoolahan's effort was ruled out for offside.
The visitors continued to press though and were rewarded eight minutes later when Hooper notched his first goal in Norwich colours.
Former Rangers man Steven Whittaker went close to adding a second, before Braga almost pulled level when Ruben Micael crashed a shot off the woodwork.
But Hooper then displayed his predatory instincts to double Norwich's lead as he reacted first to convert the rebound after Elliott Bennett's shot had been saved.
Hughton's men went in two goals to the good at the interval, but Braga controlled the early stages of the second half and pulled a goal back through Vinicius nine minutes after the restart.
Norwich keeper Mark Bunn was then forced into action as the Primeira Liga outfit chased the equaliser and eventually their pressure told when substitute Rafa finished coolly on 69 minutes.
Braga were then in the ascendancy and Yazalde Gomes Pinto nearly grabbed an unlikely win for them in the dying minutes, but his shot fizzed wide of the post.