Marvin Morgan hit the only goal of the game as Shrewsbury served up Coventry's first defeat in almost two months.
After Joe Murphy had superbly denied Matt Richards' header, Morgan netted the close-range rebound on 63 minutes to stretch improving Town's recent run to just one defeat in nine games.
Did you know?
Shrewsbury won on their first visit to the Ricoh - 49 years on from their last visit to Highfield Road in October 1963, when they lost 8-1.
New Coventry signing Leon Clarke wasted a chance to score with his first touch as a second-half substitute.
But the visitors somehow hung on to complete a double over the Sky Blues.
Clarke was again denied by Matt Richards' goalline clearance before an incredible late double save from Town keeper Chris Weale thwarted both Gary McSheffrey, who had earlier hit the bar from 25 yards, and Clarke again.
The Sky Blues' 18-goal top scorer David McGoldrick, who returned after suspension, drew a blank in his final game on loan from Nottingham Forest.
Coventry's first defeat in 10 matches slips them down to 11th in League One, while Shrewsbury's first away win of the campaign helps them climb a place to 18th - now seven points clear of trouble.
VIEW FROM THE DRESSING ROOM
Sky Blues boss Mark Robins told BBC Coventry and Warwickshire:
"We were nearly-men today. Whilst we're disappointed, we mustn't over-react. We've created a lot of chances and not taken any of them. It's as simple as that.
"We should have at least had two or three goals. We could easily have got five. We didn't, and we conceded a poor one. We didn't shut it out at the other end. That was the disappointment for me.
"There wasn't the urgency or tempo. We've done brilliantly and we've been on a good run. That run has come to an end now, which isn't the way we wanted to start the new year but we can't make too much of it. We've got to dust ourselves off and get on with the easy trip to Tottenham next weekend."
Live Text Commentary
Full Time The match has reached full-time.90:00 +3:19
Carl Baker takes a shot. Chris Weale makes a save.90:00 +1:41
Blair Adams takes the direct free kick.90:00 +1:41 Substitution
Substitution Jon Taylor leaves the field to be replaced by Yado Mambo.90:00 +1:41
Foul by Asa Hall on David McGoldrick, free kick awarded.90:00 +1:22
Cyrus Christie delivers the ball, blocked by Matthew Richards.89:55
Tom Bradshaw takes a shot. Joe Murphy makes a save.88:26
Tom Bradshaw concedes a free kick for a foul on William Edjenguele. Joe Murphy takes the free kick.86:23
The referee blows for offside. Darren Jones takes the indirect free kick.85:14
Foul by Richard Wood on Tom Bradshaw, free kick awarded. Direct strike on goal from the free kick comes in from Matthew Richards, save by Joe Murphy.83:59 Substitution
Substitution Tom Bradshaw is brought on as a substitute for Luke Rodgers.83:22
Foul by Carl Baker on Darren Jones, free kick awarded. Chris Weale takes the indirect free kick.82:28
Darren Jones takes the indirect free kick.82:28 Substitution
Substitution Franck Moussa goes off and Adam Barton comes on.82:28
Luke Rodgers fouled by Blair Adams, the ref awards a free kick.82:02
Gary McSheffrey decides to take a short corner.81:26
David McGoldrick takes a shot. Save by Chris Weale.81:01
Gary McSheffrey takes a shot. Chris Weale makes a fantastic save.80:12
Carl Baker has an effort at goal from outside the box missing to the wide left of the goal.79:49
Luke Rodgers is caught offside. William Edjenguele takes the free kick.
Luke Rodgers is caught offside. Richard Wood takes the free kick.77:49
Shot comes in from Luke Rodgers from the free kick.77:34
Free kick awarded for an unfair challenge on Marvin Morgan by Richard Wood. Strike comes in from Luke Rodgers from the free kick.76:20
Outswinging corner taken by Gary McSheffrey from the left by-line, David McGoldrick takes a shot. Connor Goldson makes a clearance.75:22
Marvin Morgan is caught offside. Free kick taken by William Edjenguele.74:13
Shot on goal by Jon Taylor from just inside the area goes over the target.73:55
Outswinging corner taken right-footed by Matthew Richards from the right by-line.73:20
The official flags Luke Rodgers offside. Joe Murphy takes the indirect free kick.72:34
Robert Purdie takes a shot. Save by Joe Murphy.71:39
Darren Jones takes the indirect free kick.71:39 Substitution
Substitution Steven Jennings leaves the field to be replaced by James Bailey.71:39
Connor Goldson fouled by Gary McSheffrey, the ref awards a free kick.69:30
Blair Adams produces a left-footed shot from close in which goes wide of the left-hand upright.67:43
Unfair challenge on Blair Adams by Asa Hall results in a free kick. William Edjenguele takes the indirect free kick.66:58
Shot by Gary McSheffrey from deep inside the penalty area misses to the left of the goal.65:50
The referee blows for offside. William Edjenguele takes the free kick.62:47 Goal scored
Goal! - Marvin Morgan - Coventry 0 - 1 Shrewsbury Marvin Morgan finds the net with a goal from close in low into the middle of the goal. Coventry 0-1 Shrewsbury.62:23
Luke Rodgers takes a shot. Joe Murphy makes a brilliant save.61:04
Close range header by Asa Hall goes over the crossbar.60:07
Free kick awarded for an unfair challenge on Marvin Morgan by Richard Wood. Direct free kick taken by Matthew Richards.59:21
Asa Hall has an effort at goal from just inside the box that misses to the right of the goal.58:14
Carl Baker produces a left-footed shot from deep inside the six-yard box which goes wide of the right-hand post.56:47
Corner taken by Jon Taylor from the right by-line.55:40
Outswinging corner taken right-footed by Jon Taylor played to the near post, Carl Baker makes a clearance.55:20
Luke Rodgers produces a cross.54:05
Headed effort from inside the penalty area by Leon Clarke misses to the right of the target.53:05 Substitution
Substitution Leon Clarke comes on in place of John Fleck.52:34
Effort on goal by Gary McSheffrey from deep inside the penalty area misses to the right of the target.51:05
Darren Jones takes a shot. Save by Joe Murphy.50:38
Free kick awarded for an unfair challenge on Marvin Morgan by William Edjenguele. Matthew Richards restarts play with the free kick.50:02
John Fleck takes a outswinging corner to the near post.49:31
Gary McSheffrey takes a shot. Blocked by Darren Jones.48:59
Shot by Blair Adams from 20 yards. Comfortable save by Chris Weale.47:12
The ball is swung over by Blair Adams, clearance by Matthew Richards.46:59
Cyrus Christie delivers the ball, clearance by Connor Goldson.45:01
The referee gets the second half underway.45:00 +4:03 Half time
Half Time The referee blows for half time.45:00 +3:12
Luke Rodgers fouled by Steven Jennings, the ref awards a free kick. Chris Weale restarts play with the free kick.45:00 +1:41
Free kick awarded for an unfair challenge on Robert Purdie by David McGoldrick. Joe Jacobson restarts play with the free kick.45:00 +0:59
John Fleck takes a shot. Save by Chris Weale.43:44
Asa Hall takes a shot. Steven Jennings gets a block in.40:47
Cyrus Christie concedes a free kick for a foul on Marvin Morgan. Joe Jacobson restarts play with the free kick.38:05
Joe Jacobson sends in a cross, Marvin Morgan produces a right-footed shot from deep inside the penalty box which goes wide of the left-hand post.37:28
Short corner worked by Gary McSheffrey.36:52
Corner taken short by John Fleck.36:28
Franck Moussa takes a shot. Save by Chris Weale.35:40
Blair Adams takes a shot. Chris Weale makes a comfortable save.34:18
Unfair challenge on Richard Wood by Luke Rodgers results in a free kick. Richard Wood takes the direct free kick.33:42
The ball is sent over by Joe Jacobson.33:22
Steven Jennings concedes a free kick for a foul on Luke Rodgers. Matthew Richards restarts play with the free kick.32:34
John Fleck takes a shot. Matthew Richards gets a block in.31:55
Foul by Darren Jones on David McGoldrick, free kick awarded. Free kick crossed left-footed by Gary McSheffrey from left channel, Jermaine Grandison makes a clearance.31:31
Connor Goldson delivers the ball, save made by Joe Murphy.29:53
Shot from just outside the box by Robert Purdie misses to the right of the target.29:32
The ball is swung over by Connor Goldson, Richard Wood manages to make a clearance.28:15
John Fleck has an effort at goal from just inside the box that misses to the left of the goal.27:24
Marvin Morgan challenges Carl Baker unfairly and gives away a free kick. Free kick taken by Joe Murphy.24:43
Asa Hall has a headed effort at goal from close range which goes wide of the left-hand post.22:38
John Fleck challenges Asa Hall unfairly and gives away a free kick. Darren Jones takes the free kick.21:44
Inswinging corner taken right-footed by John Fleck from the left by-line, save by Chris Weale.20:39
Corner from left by-line taken by Gary McSheffrey.19:49
Gary McSheffrey takes a shot. Save by Chris Weale.19:05 Substitution
Substitution Aaron Wildig leaves the field to be replaced by Asa Hall.16:46
The ball is sent over by Blair Adams.14:09
Centre by John Fleck, Joe Jacobson manages to make a clearance.12:13
A cross is delivered by Jon Taylor.8:54
Luke Rodgers takes a shot. Joe Murphy makes a save.8:25
Marvin Morgan takes a shot. William Edjenguele gets a block in.7:03
Gary McSheffrey produces a cross, Carl Baker takes a shot. Chris Weale makes a save.6:52
The ball is delivered by Carl Baker.4:35
Free kick awarded for an unfair challenge on John Fleck by Marvin Morgan. Free kick taken by William Edjenguele.3:51
David McGoldrick is flagged offside by the assistant referee. Free kick taken by Chris Weale.3:19
Franck Moussa takes a shot. Darren Jones gets a block in.2:22
Carl Baker delivers the ball, Connor Goldson makes a clearance.1:41
Marvin Morgan challenges Gary McSheffrey unfairly and gives away a free kick. Gary McSheffrey takes the free kick.0:17
Effort from deep inside the area by David McGoldrick misses to the right of the goal.0:00
The referee gets the game started.
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