The country who ended England's Euro 2008 hopes looked set to claim another British scalp when Portsmouth's Nico Kranjcar claimed the opener early on before Miller ensured an encouraging start to Burley's tenure.
The build-up had been dominated by the withdrawals which had left Burley's squad decimated for his opening game.
The loss of James McFadden was undoubtedly a blow, while Barry Robson and Stephen Pearson may well have had a part to play had they been available for selection.
Causing the biggest stir, though, was the absence of the Rangers quartet of Barry Ferguson, Christian Dailly, Lee McCulloch and Allan McGregor just a few days before a crucial match against Celtic that the majority were expected to report fit for.
The captain's armband was worn for the first time by Stephen McManus in the absence of Ferguson, with the other half of the Old Firm well represented with Gary Caldwell, Paul Hartley and Scott Brown also named in the team.
There was also a starting role for Steven Fletcher, allowing the Hibernian forward to mark his 21st birthday with his first Scotland cap, but he lasted only until half-time.
A constant downpour all day did little to help boost the crowd of just over 28,000 but it was an early opener from Croatia, rather than the weather, which threatened to put a dampener on the match.
Slaven Bilic's men were not off the mark quite as quickly as Italy in the last game at Hampden, but their 10th-minute opener was a blow all the same.
Luka Modric supplied the pass and Craig Gordon appeared to be caught cold in the Scotland goal as Kranjcar rifled high into the middle of the net from 25 yards.
To their credit, Scotland refused to crumble. Miller came off worse in a tussle with Josip Simunic and nodded over from Shaun Maloney's resultant free-kick, before restoring parity with half an hour gone.
The Derby striker raced onto a long ball down the left flank from Steven Fletcher before despatching an angled drive into the back of the net despite the best efforts of Simunic to block the effort.
Robert Kovac should have cleared the danger before the ball reached Miller but failed to make the interception and was ruthlessly punished.
Kranjcar had another go with a long-range shot in an attempt to restore Croatia's advantage before the interval but, this time, his efforts ended in failure with Gordon up to the task and smothering with ease.
Brown was the first of six names into the referee's book for a foul on Danijel Petric before the end of the first half.
But a more worrying sight was Nico Kovac's crunching tackle on the Celtic midfielder moments later, which also earned the Croatia captain a yellow card.
However, Brown emerged for the second half to the relief of both club and country, with the withdrawal of Steven Fletcher for Gavin Rae the only substitution from Scotland at half-time.
In fact, it was Brown who enjoyed the first real chance after the restart, his low shot whistling narrowly past the post, before a Miller header from Maloney's corner was cleared off the line by Danijel Pranjic.
At the other end, only some fine goalkeeping from Gordon prevented Scotland from falling behind again.
Kranjcar's shot was flicked on by Olic but the Sunderland goalkeeper stood tall to block before Caldwell hooked to safety with Olic loitering for the rebound.
Gordon then came to the rescue again with a brilliant save at the near post to deny substitute Igor Budan who charged in from the left side of the penalty area.
Jay McEveley, Gary Teale, Russell Anderson, Graham Alexander and Kris Boyd all came off the bench before the end for a taste of the action, with the introduction of Boyd prompting the biggest reaction from the crowd who were still hopeful of a winner.
His stray boot did catch the head of the unfortunate Vedran Corluka late on but it was not quite the knockout blow Scotland had in mind.
The Rangers striker, who hit a double for his club at Hampden in the recent CIS Insurance Cup final, was then denied by an excellent save from goalkeeper Stipe Pletikosa as the game ended all square.