The Canaries' new boys struck their first goals for the club in the 38th and 44th minutes before Bolton had Ivan Klasnic sent off for an apparent head-butt.
But the visitors' long-awaited victory - their first since winning at Crystal Palace in 1994 - did not come easy as the 10-man Trotters reduced the deficit with a Martin Petrov penalty.
And Norwich keeper John Ruddy had to make a brilliant point-blank save to deny Bolton substitute David Ngog in injury time as home keeper Jussi Jaaskelainen also pressed forward.
With both sides smarting from tough losses the previous weekend it was no surprise the opening half hour was a tame affair which the Canaries' sharpness just about shaded.
Norwich boss Paul Lambert had made six changes to the side humbled at home by West Bromwich Albion while Coyle remained more loyal to the side beaten out of sight by Manchester United.
Elliott Bennett forced Jaaskelainen to palm his long-range effort over the bar on six minutes while the home side's story was one of misplaced passes and flat-footed defending.
Steve Morison outjumped both Gary Cahill and the gangly Zat Knight to flash an eighth-minute header just wide after referee Howard Webb had appeared to over-rule the linesman's flag.
Kyle Naughton blocked Bolton's first chance from Dedryck Boyata on 14 minutes but it was the visitors, largely through the fleeting Bennett down the right, who held the upper hand.
The home side showed more purpose on 35 minutes when Nigel Reo-Coker's clever ball released Kevin Davies down the left and his dangerous in-swinging cross was palmed out by Ruddy.
The visitors were good value for their 38th-minute lead which came when Leon Barnett headed down a David Fox corner to Morison, who squared for Pilkington to squeeze the ball home off the post.
And six minutes later the Canaries grabbed their second when Fox's free-kick from deep on the right found the head of Johnson who powered the ball past Jaaskelainen.
Just when it seemed it could not get any worse for Bolton, Klasnic was needlessly sent off on the stroke of half-time for an apparent head-butt on Marc Tierney.
Norwich dominated the opening stages of the second period and more goals looked on the cards, with Pilkington almost taking advantage of Boyata's stumble when clearing a Morison cross.
But new boy Ngog, hauled on at half-time as a replacement for the lacklustre Davies, lent his side more attacking intent and it paid off with a 63rd-minute lifeline.
Ngog started the move which ended in Boyata being tripped in the box by Barnett, and after Webb pointed to the spot Martin Petrov stepped up to drill a low spot-kick past Ruddy.
The goal belatedly breathed life into Coyle's men who continued to storm forward, Boyata finding substitute Ngog whose shot was deflected out for a corner.
Inevitably, Bolton's push for an equaliser left spaces at the back but the Canaries were failing to exploit them with substitute Grant Holt in particular failing to find a way through.
Boosted by the busy Ngog, Coyle's men began to look much more threatening and City began to show signs of nerves as they moved closer to their away-win milestone.
Bennett headed a dangerous Paul Robinson cross behind for a corner in the final minute then in injury time Ngog came agonisingly close to handing Bolton redemption.