In a highly-charged city derby full of colour, passion and extreme aggression on the field and in the packed stands, Roma prevailed to move a point above champions Inter Milan with just four games remaining.
"It's the most beautiful thing that exists in football. With my two goals I'm even happier," Vucinic told Sky TV after Roma extended their unbeaten run in Serie A to 24 games.
The chance of fourth scudetto for Roma looks ever more likely having been unthinkable in February when Inter held a nine-point lead.
Tommaso Rocchi calmly put Lazio ahead on 14 minutes after a well-timed run and the strugglers, still not clear of relegation, should have been further in front but Julio Sergio saved Sergio Floccari's penalty just after the break.
Lazio wing-back Aleksandar Kolarov was felled for the soft penalty but he was the one conceding a debatable spotkick shortly after, allowing Vucinic to fire in the equaliser.
The Montenegro forward then sent the Roma fans into ecstasy when he blasted home a free-kick midway through the second half which went right through the centre of a weak Lazio wall.
Roma boss Claudio Ranieri took a big risk at halftime when he took off Francesco Totti and Daniele De Rossi, two Rome-born talismen, but his tactical gamble turned into a masterstroke.
LEONARDO RUMOURS
AC Milan's Serie A title hopes were hanging by the shortest of short threads after Giampaolo Pazzini's injury-time header sealed a 2-1 home win for Champions League hopefuls Sampdoria.
The defeat comes at the end of a difficult week for Milan, with rumours swirling that rookie coach Leonardo is on the verge of leaving after just one season despite repeated denials.
Third-placed Milan, who lie seven points behind Roma, began well and were rewarded when striker Marco Borriello nodded in.
Antonio Cassano equalised with a penalty early in the second half after Milan's Daniele Bonera was dismissed but the Rossoneri then wasted a host of chances.
Baby-faced forward Pazzini punished them deep into stoppage time when he produced the type of trademark header which could rocket him into Italy coach Marcello Lippi's plans.
Sampdoria stand two points clear in the fourth and final Champions League qualifying spot after leapfrogging Palermo, who were held to a 2-2 draw at Cagliari.
Sixth-placed Napoli, five behind Samp, won 2-1 at Bari thanks to Ezequiel Lavezzi's double.
The result was a further dagger to the hearts of Juventus fans, whose famous club have sunk to seventh, six points behind the Champions League spots, after Friday's 2-0 defeat at Inter.
Bottom side Livorno, who lost 2-0 at Chievo on Saturday, will have to wait at least another week to be put out of their misery and relegated after Bologna could only draw 1-1 at Udinese following Antonio Di Natale's late leveller.
