The Stoke City loanee netted either side of the break to earn the Canaries a victory which takes them level with Derby County at the top of the table, although Lee Chung-yong's strike gave them a late scare on Halloween.
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Norwich's breakthrough started and finished with Jerome, who won a flick-on above Matt Mills before racing away from the defender to collect a pass from Jonny Howson and calmly poke past Andy Lonergan.
Redmond's influence grew as the game went on, with the winger cutting inside from the right to shoot only a few yards wide prior to the break, before enjoying a lightning start to the second half.
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The England Under-21 international forced Lonergan into an awkward save at the near post with a misdirected cross and then fired a powerful shot slightly high after Bolton had failed to clear a corner.
He came within inches of doubling Norwich's lead on 57 minutes when he exchanged passes with Kyle Lafferty and rolled a shot from a tight angle towards the bottom corner, but Lonergan smartly tipped onto the post.
The Canaries were two up shortly afterwards though, as Jerome took his tally to nine for the season in all competitions by heading in what was just one of several dangerous Gary O'Neil deliveries at the near stick.
They should have been out of sight on 71 minutes, but Lonergan was single-handedly keeping Wanderers in the match and his impressive reflex save kept out Whittaker after Redmond had found him with a cutback.
Norwich continued to push forward in search of a third goal which would have taken them top of the table outright, and were caught out when Mark Davies released substitute Max Clayton for Bolton's best chance.
The former Crewe Alexandra forward replaced the anonymous Jermaine Beckford, who is still without a league goal this season, and was through one on one with Ruddy but pulled a left-footed shot horribly wide.
Neil Lennon's side did grab a goal back as a defensive mix-up between Russell Martin and Martin Olsson allowed Lee to pounce and cleverly squeeze the ball past Ruddy with four minutes left on the clock.
However, Norwich hung on to win for the first time since September and inflict a second loss on Lennon as Bolton boss.