Scotland gave their best performance in several years to beat the world's fourth best team on their own turf.
It was a display full of self-belief, guts and quality from Gordon Strachan's men to record their first win of the World Cup qualifying campaign.
Robert Snodgrass scored the crucial goal, latching onto a loose ball to prod it past Stipe Pletikosa.
Croatia pressed for an equaliser, but failed to bring out a save of any note from Allan McGregor.
The contrast between this Scots performance and those that have preceded it was remarkable, with Russell Martin, James McArthur and Alan Hutton perhaps the pick of a heroic bunch.
Of course, it comes much too late to make any impact in the group, but it ensures Scotland will be in pot four for the draw for Euro 2016 and gives the Scotland management team something concrete to build on for the future.
They set the tone in the opening stages with some confident passing and dogged closing-down to ensure the Croatians were unable to seriously threaten McGregor's goal.
The same could be said of Pletikosa - the home keeper barely touching the ball before his side found themselves a goal down after 26 minutes.
The goal had a touch of fortune about it, but Scotland will feel they were rewarded for their endeavour, as Shaun Maloney's attempted pass broke off a Croatian leg and the ball fell kindly for Snodgrass, who stretched to nudge it past Pletikosa.
The keeper took an accidental boot in the face as Snodgrass beat him to the ball and required lengthy treatment before continuing, but he was rattled, much like the rest of his team-mates.
That good Scots work was almost undone, though, when Grant Hanley was short with a pass-back, forcing McGregor to take evasive action to deny Mario Mandzukic and when the ball broke to Sammir, Hanley breathed a sigh of relief as he lifted the ball over the bar.
There was further concern for the visitors as Ivica Olic sold Alan Hutton a beautiful dummy, but Russell Martin dived in and forced Olic to shoot wide and moments later the Norwich defender performed further heroics to keep a Darijo Srna shot from crossing the line.
Olic and Barry Bannan both blazed fierce shots just off target at the outset of the second half, but Croatia missed a fantastic opportunity to level the match after an hour's play.
Olic fired in a terrific cross from the left, which was begging to be tapped over the line, but Mandzukic arrived a fraction of a second too late to get the crucial touch.
Croatia continued to see more of the ball, but Scotland's work ethic was phenomenal, closing down their opponents while retaining their shape and making it extremely difficult for the home side to create clear-cut chances.
Indeed, McGregor didn't have to dirty his gloves for the remainder of the match as the Scots held on for their most momentous win since the 2007 victory over France in the Parc des Princes.
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Live Text Commentary
Full Time The referee signals the end of the game.90:00 +2:38
Ivica Olic delivers the ball.90:00 +1:40
Steven Whittaker restarts play with the free kick.90:00 +1:40 Booking
Booking Steven Whittaker shown a yellow card.90:00 +1:10
Darijo Srna gives away a free kick for an unfair challenge on Craig Conway.86:56 Substitution
Substitution Niko Kranjcar replaces Mario Mandzukic.80:04
Mateo Kovacic has an effort at goal from just outside the area which goes wide of the left-hand post.79:55
The ball is sent over by Ivica Olic, Russell Martin makes a clearance.78:34
Josip Simunic gives away a free kick for an unfair challenge on Alan Hutton. Free kick taken by Allan McGregor.77:51
Gordon Schildenfeld takes the free kick.77:51 Booking
Booking Booking for James McArthur.77:38
James McArthur gives away a free kick for an unfair challenge on Ivan Rakitic.76:57
Free kick taken by James Morrison.76:57 Booking
Booking Ivan Rakitic receives a caution.76:55
Foul by Ivan Rakitic on Craig Conway, free kick awarded.75:24
The ball is delivered by Ivan Rakitic, Mario Mandzukic produces a header from deep inside the six-yard box that clears the crossbar.74:26 Substitution
Substitution Shaun Maloney goes off and Craig Conway comes on.70:01
Corner taken right-footed by Darijo Srna, save by Allan McGregor.69:08 Substitution
Substitution Nikola Kalinic comes on in place of Ivan Strinic.68:07
Mateo Kovacic takes a shot. Allan McGregor makes a save. The referee blows for offside against Da Silva Eduardo. Allan McGregor takes the indirect free kick.
Corner taken short by Ivan Rakitic.67:22
Jordan Rhodes gives away a free kick for an unfair challenge on Mateo Kovacic. Darijo Srna takes the direct free kick.66:00
The official flags Mario Mandzukic offside. Allan McGregor takes the indirect free kick.65:01
Foul by Ivan Strinic on Alan Hutton, free kick awarded. Robert Snodgrass crosses the ball in from the free kick.64:43
Free kick awarded for an unfair challenge on Alan Hutton by Da Silva Eduardo. Free kick taken by Grant Hanley.64:00
Da Silva Eduardo takes a shot. Save made by Allan McGregor.62:35 Substitution
Substitution Jordan Rhodes replaces Leigh Griffiths.62:35 Substitution
Substitution Steven Naismith is brought on as a substitute for Barry Bannan.62:13
Effort on goal by Mario Mandzukic from inside the area goes harmlessly over the bar.61:39
Jorge Sammir has an effort from just inside the box that misses to the left of the goal.60:19
Ivica Olic sends in a cross.56:36
Gordon Schildenfeld challenges Leigh Griffiths unfairly and gives away a free kick. Leigh Griffiths crosses the ball from the free kick right-footed from left wing, Darijo Srna makes a clearance.55:57
The ball is crossed by Alan Hutton, Barry Bannan produces a left-footed shot from the edge of the box and misses to the right of the target.54:47 Substitution
Substitution (Croatia) makes a substitution, with Da Silva Eduardo coming on for Ivan Perisic.54:05
Ivica Olic takes a shot from just outside the penalty area which clears the crossbar.52:11
Outswinging corner taken left-footed by Ivan Rakitic.49:12
Ivan Rakitic sends in a cross, Ivan Perisic takes a shot. Allan McGregor makes a save.47:26
Ivan Rakitic produces a right-footed shot from just outside the area that goes harmlessly over the bar.45:01
The referee starts the second half.45:00 +5:20 Half time
Half Time The ref blows to end the first period.45:00 +5:17
The ball is sent over by Ivan Strinic, clearance made by Russell Martin.45:00 +2:16
Robert Snodgrass decides to take a short corner.45:00 +2:16 Booking
Booking Allan McGregor receives a caution for time wasting.45:00 +2:02
The ball is crossed by Darijo Srna.45:00 +1:26
Corner from the right by-line taken by Darijo Srna, clearance made by Grant Hanley.45:00 +0:55
A cross is delivered by Darijo Srna, Grant Hanley makes a clearance.45:00 +0:07
Free kick awarded for a foul by Mario Mandzukic on Grant Hanley. Free kick taken by Allan McGregor.44:14
Shot from deep inside the area by Ivica Olic clears the crossbar.42:24
Foul by Josip Simunic on Robert Snodgrass, free kick awarded. Shaun Maloney delivers the ball from the free kick right-footed from right wing, clearance by Josip Simunic.39:51
Ivan Perisic has a shot and went wide right of the goal.38:44
Ivan Rakitic has a headed effort at goal from close in which goes wide right of the target.35:58
Effort on goal by Jorge Sammir from just inside the box goes harmlessly over the target.35:04
Ivan Strinic gives away a free kick for an unfair challenge on Robert Snodgrass. Free kick crossed by Leigh Griffiths, save by Stipe Pletikosa.34:10
The ball is swung over by Ivan Rakitic, Allan McGregor makes a save.32:54
Mario Mandzukic concedes a free kick for a foul on Russell Martin. Free kick taken by Alan Hutton.32:15
Foul by Darijo Srna on Shaun Maloney, free kick awarded. Free kick taken by Shaun Maloney.30:57
Shot on goal by Ivan Perisic from just inside the area goes over the target.25:34 Goal scored
Goal! - Robert Snodgrass - Croatia 0 - 1 Scotland Robert Snodgrass gets on the score sheet with a goal from close in low into the middle of the goal. Croatia 0-1 Scotland.22:50
The ball is sent over by Darijo Srna, clearance made by Alan Hutton. Inswinging corner taken by Ivan Rakitic. Grant Hanley fouled by Mario Mandzukic, the ref awards a free kick. Allan McGregor takes the free kick.22:38
The ball is delivered by Darijo Srna, Steven Whittaker gets a block in.21:23
Shot from just outside the box by Ivan Perisic goes over the crossbar.19:24
The assistant referee signals for offside against Ivica Olic. Allan McGregor takes the indirect free kick.16:09
Outswinging corner taken by Darijo Srna from the right by-line, clearance by Grant Hanley.12:07
Robert Snodgrass challenges Ivan Strinic unfairly and gives away a free kick. Ivan Strinic takes the free kick.10:00
James Morrison takes a shot from just outside the penalty area clears the crossbar.7:47
Robert Snodgrass fouled by Ivan Strinic, the ref awards a free kick. Shaun Maloney takes the free kick.7:15
Alan Hutton takes a shot. Blocked by Josip Simunic.6:16
Foul by Ivica Olic on James McArthur, free kick awarded. Free kick taken by Grant Hanley.5:53
Free kick awarded for a foul by Barry Bannan on Darijo Srna. Free kick taken by Darijo Srna.3:08
Darijo Srna crosses the ball.0:00
The ref blows the whistle to begin the match.
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