Fearing that historical tensions between the rival supporters might boil over into violence, Tipsarevic asked tournament organisers to move his game against Cilic away from the outside courts - where spectators can wander around as they please - and onto one of the tightly supervised show courts.
Melbourne is home to large communities of expats from the former Yugoslavian states, whose volatility was all-too-clearly demonstrated by the notorious Australian Open riot of 2007. That was the year when gangs of Serbian and Croatian fans fought a pitched battle in the elegant "garden area" of Melbourne Park.
"Normally the problem is with people who live abroad," said Tipsarevic. "And especially in Australia because it's so far away from their homeland. It's stupid to say these people love Serbia more, but they do feel nostalgic for it - and sometimes they cheer too much.
"I told the guys who are in charge of the schedule what might happen, and I'm glad they listened to me and put us on the show court, where the chance of violence is reduced. The problem is that if the Serbs and Croats pass by each other, and someone says something rude, then they will start to fight."
Tipsarevic's forebodings were borne out by the atmosphere on No 2 court, which became aggressively polarised and partisan. The pro-Cilic faction sat in the south-eastern corner, decked out in their red-and-white checked shirts. The Tipsarevic devotees camped in the western stand, wearing long capes decorated with the Serbian flag. Both groups chanted slogans and shouted obscenities in their own languages - which, fortunately, were completely unintelligible to the majority of spectators.
"The things that they were saying were really not nice," explained Cilic, who was the target of much of the abuse. "It was tough to play, of course. But I was trying to stay focused on the match and do as well as I could. When they said a couple of bad words to me, Janko told them to be quiet."
The rival fans' behaviour may have been more typical of an "Old Firm" football derby than a tennis match, but the players still maintained an impressive level of sportsmanship. Tipsarevic and Cilic came out dressed in identical kits and did all they could to avoid igniting an already inflammable situation.
"We were talking to each other when we went to the net," Tipsarevic explained, "and he told me, 'I don't know about you, but for me this is really tough, playing in these conditions.' I said, 'For me, the same.'
"Both the Serbs and the Croats were a little bit incorrect," Tipsarevic added. "They were singing songs that were nothing to do with tennis, because of the history we have between each other."
The players still put on an absorbing show, as witnessed by the long lines of spectators queuing for a seat in the stands. At 6ft 6in, Cilic is even taller and more lethal on serve than his compatriot Mario Ancic (5ft 5in), and he bombed down a fusillade of aces on the way to a two-set lead.
Tipsarevic rallied in the third set, taking advantage of his opponent's brief loss of concentration to spray a series of forehand winners. But a lucky net cord helped Cilic to steal the initiative back in the fourth, and he quickly closed out the match.
"Given all the things that were going on, the tension and provocation, I was glad to win it in four," Cilic said. "Things were getting tighter towards the end."
The police kept a close eye on the fans as they streamed out of the venue. The more hot-headed elements formed two lines in the concourse underneath the stadium, singing, gesturing and staring each other out. Happily, though, the atmosphere was closer to West Side Story than Goodfellas.
"We kept an eye on the match but no ejections were needed and the police have been very happy with the way things have gone so far this week," said a spokesperson for the Victoria police. After the riots of 2007, and the incident last year when two Greek supporters were doused with pepper spray, the 2009 Australian Open has remained a non-contact sport.