Having described Turkish referee Cuneyt Cakir as an outstanding official, but one happy to brandish yellow and red cards for any kind of misdemeanour, Stimac said his players must keep cool heads and their studs down in the Group A clash in Zagreb.
"We saw a few weeks ago that this referee does not hesitate to punish ruthlessly any kind of offence and hence I've told the players to refrain from rash tackles," said Stimac, referring to Cakir's decision to send off Manchester United forward Nani in their Champions league defeat by Real Madrid earlier this month.
"I've also told them to avoid any kind of arguing with the officials because the last thing we need in a game like this is to shoot ourselves in the foot," he told a news conference at Dinamo's Maksimir stadium on Thursday.
Unbeaten Croatia sit behind Belgium on goal difference on 10 points from four matches. Serbia are third on four points.
Mihajlovic stressed he would have zero tolerance for any thoughtless acts by his players.
"If any of my players were to be sent off for dissent or a mindless tackle that merits a red card, they can forget about being part of the national team as long as I am in charge," he said.
"This is a very special match and we will behave impeccably, that's all we can do to make sure this event is remembered for all the right reasons as we expect football to come to the fore and politics to take a back seat."
Friday's fixture, which will be played under tight security, will be the first meeting between Croatia and Serbia as independent nations since the violent break-up of the former Yugoslavia.
NO AWAY FANS
Both have agreed not to take away fans to either match, with the reverse encounter set for Sept. 6 in Belgrade, while Stimac and Mihajlovic appealed to fans to support their respective nations in a sportsmanlike manner.
"I hope Croatian fans are intelligent enough to behave tomorrow and that our fans will do the same in the return match in Belgrade, because any outburst of hatred can only be to the detriment of the home team in either match," said Mihajlovic.
Defeat would leave Serbia with an almost impossible task of catching up with the leaders and pile more pressure on Mihajlovic, who dismissed any talk of resignation if his team lost.
"I am not a quitter and having refused to resign in more difficult situations I will certainly not step down at a time when we are in the process of building a team capable of making an impact in the future," he said.
Stimac, who named an adventurous 4-4-2 formation with playmaker Luka Modric as well as forwards Niko Kranjcar and Ivan Rakitic behind strikers Mario Mandzukic and Ivica Olic, was confident his team would live up to the billing of being strong favourites.
"We are confident because we have more players than Serbia who have big games for their clubs every week, we know what Serbia's strengths and weaknesses are and we are looking forward to what should be an enjoyable match," he said.