Norwich earned their first win of the season at the expense of 10-man Bolton who lost their third successive game.
The Canaries' first-half pressure paid off when Anthony Pilkington prodded home from close range on 37 minutes, followed five minutes later by a classy header from Bradley Johnson.
Bolton were down to 10 when Ivan Klasnic saw red for headbutting full-back Marc Tierney.
Martin Petrov's penalty reduced the deficit but Norwich held on.
Defeat was self inflicted - Coyle
It was the fifth conceded by the side in as many games - a Premier League record - and deftly converted by Petrov after second-half substitute David Ngog was barged in the back by Leon Barnett.
Victory was Norwich's first away win in the top flight for 17 years, and while manager Paul Lambert has complained of their treatment at the hands of referees, there were no complaints about the penalty.
The consolation goal will prove little comfort for Bolton fans who greeted part of their team's first-half performance with groans.
The Norwich fans however, among them Shadow Chancellor Ed Balls, were left buoyant.
Searching runs and a shot from Elliot Bennett, as well as a Russell Martin header, saw Norwich start off brightly, sending a signal of intent to a Bolton side now labouring under four straight league defeats.
Norwich: Paying the penalties
Norwich now hold the Premier League record for the most consecutive games in which penalties were given against them
The previous record was held by Wimbledon with four
Eight minutes before the break Leon Barnett diverted a corner back into a mass of bodies, among them Pilkington who spun and poked the ball home.
The Bolton defence remained shaky as Johnson rose to head a cross from the right wing into the bottom left-hand corner, leaving a stunned Jussi Jaaskelainen on his knees and staring into his net.
By the end of the first half the fans' displeasure was audible and Coyle responded by sending on Chris Eagles and David Ngog.
Norwich appeared to have the game wrapped up after Klasnic walked following a straight red card from referee Howard Webb.
Lambert - we were excellent
The forward had been waving his arms in the direction of Marc Tierney and received a nudge in the melee. He responded by flashing his forehead in Tierney's direction, the latter going down easily after what appeared to be slight contact.
There was drama near the end of the game when Canaries goalkeeper John Ruddy acrobatically saved a point-blank header from Ngog seconds before the whistle.
Bolton Wanderers manager Owen Coyle:
"To concede the two goals from set-plays certainly wasn't good enough. We're all designated markers and we haven't done well enough in that department.
"My concern is when we concede soft goals like we did today. It's not as if someone has beaten two or three players and hit it into the top corner - this was self inflicted.
"Even at 2-0 we can still find a way back into the game and then comes Ivan's sending-off. There's no doubt it's a disappointing game and we have to do far better from start to finish."
Norwich City manager Paul Lambert:
"I've never had a problem with confidence. They seem to bounce back whether they draw or get beaten, and that is testament to the way they played today.
"I thought we were really comfortable up to the penalty, then Bolton threw everything at us.
"That put us on the back foot for five or 10 minutes but we fought through."
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