Jacob Murphy fired in a 25-yard shot, his first goal for the club, to set the Canaries on their way on 12 minutes.
Further goals from Wes Hoolahan and Cameron Jerome then put Alex Neil's men three up inside 25 minutes.
Steven Naismith added a fourth before Rovers half-time substitute Anthony Stokes headed a debut Ewood Park goal.
Norwich failed to score in five of their last six games in the Premier League - but Alex Neil's side wasted no time in putting that right as they enjoyed their first opening-day victory in 14 years.
In new Blackburn boss Coyle's first game in charge since succeeding former Norwich manager Paul Lambert, his outclassed side were fighting a massive uphill battle before the new season was even half an hour old.
After scoring 10 times last season on loan at Coventry, 21-year-old Murphy netted just 12 minutes into his Canaries debut when he wriggled clear from Adam Henley and was allowed to turn before blasting home a fabulous strike from well outside the box.
Five minutes later, Hoolahan's left-foot shot found the bottom left corner before Jerome found the net for number three. And, on 57 minutes, Naismith's left-foot shot found the bottom right corner.
Stokes' late consolation could not prevent Norwich's third win at Blackburn in 19 visits, and their second in a row, having won 2-1 on their last trip to Ewood in February 2015.
Blackburn Rovers manager Owen Coyle: "I don't think it's one that we wanted, envisaged or anticipated. We started the first 10 minutes very well, on the front foot, and for all intents and purposes, we looked fine.
"Then the lad scores a wonder goal. I'm not sure he'll score too many goals as good as that in his career, but that's the quality Norwich City have.
"They've been clinical and ruthless and punished us for every mistake we've made. Having said that, it's important that in those areas where the Hoolahans and Naismiths are popping the ball off, that we get pressure on the ball and get that tackle in.
"With all due respect, with the first three goals and even the fourth one, we allowed them time to play and, when good players pass and move at pace, it causes anybody problems."
Norwich City boss Alex Neil: "Jacob Murphy earned his start. I played him against Hannover last week. I took him off because I had to solidify the middle of the pitch.
"I spoke to him throughout the week and said 'I'm not now fixing Hannover, I'm preparing to beat Blackburn.' He's responded. It's a fantastic strike.
"He's got the pace to terrify defenders, as he showed with his goal. He's got something in his locker where he can win a game with his quality.
"We wanted to play in a manner which people are going to sit up and take notice of us and know that we mean business this season, and we did all that, which was really pleasing."
Match ends, Blackburn Rovers 1, Norwich City 4.
Second Half ends, Blackburn Rovers 1, Norwich City 4.
Attempt missed. Timm Klose (Norwich City) header from the centre of the box misses to the left. Assisted by Alex Pritchard with a cross following a corner.
Corner,  Norwich City. Conceded by Gordon Greer.
Corner,  Norwich City. Conceded by Gordon Greer.
Attempt blocked. Cameron Jerome (Norwich City) right footed shot from a difficult angle on the right is blocked. Assisted by Steven Naismith.
Offside, Blackburn Rovers. Adam Henley tries a through ball, but Danny Graham is caught offside.
Offside, Blackburn Rovers. Danny Graham tries a through ball, but Liam Feeney is caught offside.
Foul by Ivo Pinto (Norwich City).
Ben Marshall (Blackburn Rovers) wins a free kick on the left wing.
Corner,  Blackburn Rovers. Conceded by John Ruddy.
Foul by Ivo Pinto (Norwich City).
Adam Henley (Blackburn Rovers) wins a free kick on the left wing.
Foul by Cameron Jerome (Norwich City).
Shane Duffy (Blackburn Rovers) wins a free kick in the attacking half.
Attempt missed. Darragh Lenihan (Blackburn Rovers) header from the centre of the box is too high. Assisted by Liam Feeney with a cross following a corner.
Corner,  Blackburn Rovers. Conceded by Cameron Jerome.
Corner,  Blackburn Rovers. Conceded by Cameron Jerome.
Corner,  Blackburn Rovers. Conceded by Alexander Tettey.
Foul by Alex Pritchard (Norwich City).
Anthony Stokes (Blackburn Rovers) wins a free kick in the attacking half.
Corner,  Blackburn Rovers. Conceded by Alex Pritchard.
Attempt saved. Anthony Stokes (Blackburn Rovers) right footed shot from outside the box is saved in the bottom right corner.
Youssouf Mulumbu (Norwich City) is shown the yellow card for hand ball.
Hand ball by Youssouf Mulumbu (Norwich City).
Substitution, Norwich City. Alex Pritchard replaces Wes Hoolahan.
Attempt missed. Jacob Murphy (Norwich City) right footed shot from outside the box is close, but misses to the right from a direct free kick.
Substitution, Norwich City. Youssouf Mulumbu replaces Jonny Howson.
Gordon Greer (Blackburn Rovers) is shown the yellow card for a bad foul.
Jacob Murphy (Norwich City) wins a free kick in the attacking half.
Foul by Gordon Greer (Blackburn Rovers).
Steven Naismith (Norwich City) wins a free kick in the defensive half.
Foul by Shane Duffy (Blackburn Rovers).
Foul by Jonny Howson (Norwich City).
Darragh Lenihan (Blackburn Rovers) wins a free kick in the defensive half.
Delay over. They are ready to continue.
Delay in match Adam Henley (Blackburn Rovers) because of an injury.
Cameron Jerome (Norwich City) is shown the yellow card for a bad foul.
Foul by Cameron Jerome (Norwich City).
Darragh Lenihan (Blackburn Rovers) wins a free kick on the left wing.
Norwich City made a great start to life back in the Championship following relegation as they battered Owen Coyle's Blackburn Rovers at Ewood Park.