Stimac, who turns 46 on the day of the game, steered the Croatians to a 2-0 win over Serbia in the reverse fixture in Zagreb and said he expected the same kind of mature performance from his men in the cauldron of Red Star Belgrade's Marakana stadium.
"We needn't worry about Serbia if we play at our usual level and beating them tomorrow would be the ideal birthday present because we will be up against a good team with a huge motive to give their fans something to cheer," Stimac told a news conference on Thursday.
"We know what the chinks in Serbia's armours are and we will try to put them under pressure from the off like we did in Zagreb although we won't throw caution to the wind.
"I know we are not going to get a red-carpet reception here but I am not bothered because my team is full of players who have performed in bigger stadiums than Red Star's more than a few times in their careers," added Stimac.
The Serbian FA said more than 4,000 riot and regular police would be deployed in and around the 55,000-seater stadium where the capacity has been cut to 40,000 for security reasons even though both soccer federations agreed not to take away fans to either match.
Croatia have 16 points from seven games, three fewer than group leaders Belgium and nine more than third-placed Serbia who must win to keep alive any hopes of snatching a playoff berth.
A victory or a draw would leave the Croatians in the hunt for an automatic berth for next year's finals in Brazil but Stimac suggested he would be happy with a runners-up finish and a playoff berth.
"We are experienced enough to know we can qualify through the playoffs and although we'd like to go through automatically as group winners, we don't see the task as imperative," said the coach.
Captain Darijo Srna added: "It's Serbia who are under pressure to deliver on home soil because I know how much weight we had on our shoulders ahead of the first game in Zagreb. We have to be cool-headed and take our chances when they come."
Serbia coach Sinisa Mihajlovic, who has come under fire from fans and media after poor results left his team's chances hanging by a thread, appealed to the supporters to turn up in their droves.
"The fans can be like an extra man if they come in numbers and get behind the lads," he said.
"This is a young team and they will play at the top of their limits if the crowd gets behind them but lack of support could really dent their confidence and hamper their performance."
- Sports & Recreation