The Borussia Monchengladbach midfielder's 80th minute goal rounded off a fantastic second-half comeback by the United States to deny Slovenia the chance to progress to the last 16 of the tournament on their debut in the finals and ensure coach Bob Bradley still has his own hopes of reaching the knockout stages intact.
Bradley Jnr conjured a composed finish from close range, after Jose Altidore's header back into the penalty area picked out his team-mate's run from midfield, as USA battled back from a two-goal deficit at half-time to prevent Slovenia from making history for their tiny nation.
USA threw away a two-goal lead in the same stadium against Brazil in the Confederations Cup 12-months ago, before succumbing to a 3-2 defeat, but Landon Donovan inspired an incredible fight-back on this occasion, after Bradley made two second half changes.
And substitute Maurice Edu felt he was denied a perfectly good winning goal four minutes from time after a bizarre decision from Mali referee Koman Coulibaly, but USA will be relieved to still be in the tournament after Valter Birsa and Zlatan Ljubijankic had handed Matjas Kek's men a commanding first-half lead.
Slovenia had never been to a finals, but Kek's side have made amazing strides since he was labelled a "fool" by Slovenians for losing his first five games as coach of the national team.
If they, like the United States, had to rely on some dubious goalkeeping for their opening goal of the tournament against Algeria, there was nothing lucky about their 13th minute lead. The Jabulani ball has been heavily criticised by all 32 teams in the tournament - but you won't be hearing any complaints from Birsa.
He showed everyone how it's done with an incredible 30-yard strike after only 13 minutes that left keeper Tim Howard rooted to the spot in disbelief and the Everton man was floored again three minutes before the break when Ljubijankic sprang the offside trap.
The striker included in place of Zlatko Dedic rewarded his boss by collecting Milivoje Novakovic's excellent pass to slide his shot under the advancing Howard.
It was a bitter blow for Bradley and Co, who moments earlier had been denied an equaliser when Miso Brecko cleared off the line as Donovan was ready to pounce, but the LA Galaxy star did mark his 125th cap by reducing the arrears with a brilliant finish from a narrow angle - but it was Bradley's late show that put the smile back on his father's face.
Slovenia: (4-4-2): Handanovic S; Brecko, Suler, Cesar, Jokic; Birsa (Dedic), Koren, Radosavljevic, Kirm; Novakovic, Ljubijankic (Pecnik 75).
Subs not used: Dzinic, Ilic, Handanovic J, Krhin, Seliga, Filekovic, Komac, Stevanovic, Mavric, Matavz.
USA (4-4-2): Howard; Bocanegra, DeMerit, Onyewu (Gomez 80), Cherundolo; Donovan Torres (Feilhaber 46),Bradley, Dempsey; Altidore, Findley (Edu 46).
Subs not used: Spector, Beasley, Holden, Bornstein, Clark, Buddle, Guzan, Goodson, Hahnemann.