Following Friday's emotional 2-0 home triumph over neighbours Serbia, the Croatians came from behind to beat Wales 2-1 in Swansea on Tuesday after Stimac got the most out of his tactical substitutions in the final 30 minutes.
He threw on teenage midfielder Mateo Kovacic and 33-year old striker Ivica Olic with the gamble paying off as the former's creativity and the latter's speed turned the screw on Wales, who had taken the lead through a Gareth Bale penalty.
Defender Dejan Lovren, often criticised over costly errors for Croatia and his Ligue 1 club Lyon, justified selection with a stunning equaliser before Eduardo da Silva poked in a late winner to keep Croatia level with Belgium at the top of Group A.
Both teams are on 16 points from six matches, nine clear of third-placed Serbia as the battle for the one automatic place for the group winners in Brazil next year has been whittled down to a two-horse race.
It was a fifth win in six competitive matches for Stimac, who could not have imagined a better scenario after being jeered by fans in his native Split when Croatia were beaten 4-2 by Switzerland on his coaching debut last August.
"We made the right substitutions and ground out a hard-fought win after falling behind but it was a strange feeling to chase the game because it's the first time we had fallen behind in this qualifying campaign," Stimac told Croatian television.
"We started with Milan Badelj to rest the young Kovacic, who had a great international debut against Serbia, but Badelj was well below par and we had to make changes in order to move up a gear in the closing stages."
The Croatians are next in action at home to bottom side Scotland in June but will be without Lovren, playmaker Luka Modric and defender Vedran Corluka through suspension after all three picked up yellow cards in Swansea.
Captain Darijo Srna stressed that not having the trio was a small price to pay for what he described as a vital win to keep up the pressure on Belgium, who eked out a 1-0 home win over Macedonia.
"The victory over Serbia would have been meaningless if we had dropped points against Wales and although we will miss three players against Scotland, we should be good enough to beat them whatever first team the coach picks," he said.
"We were emotionally drained after beating the Serbians, made a poor start against the Welsh but Stimac made the right tactical adjustments and our character came through in the end."