The 24-year-old Slovenian had opened his account for the Bantams in Tuesday's 2-1 Checkatrade Trophy win against Bury, but was named among the substitutes against Shrewsbury on Saturday.
But he was introduced in the 88th minute with his side leading 1-0, and within moments of his arrival Bradford were awarded a spot-kick.
With regular penalty-taker Tony McMahon injured, Vuckic grabbed the ball and made no mistake from 12 yards to seal a 2-0 win.Ivan Toney was in the Shrewsbury side; he played the whole match and picked up a yellow card.
Sammy Ameobi was another player who made an impact from the bench on Saturday. He was brought on in the 60th minute and was in close attendance as Swindon's Brandon Ormonde-Ottewill put through his own net in the 86th minute for the only goal of the game.
Carlisle's unbeaten start continued with a 3-0 win at Morecambe; Macaulay Gillesphey played the full match. And Darlington gained a 2-2 draw at Brackley, with Paul Woolston keeping goal for the Quakers.
Alex Gilliead appeared as a 62nd-minute substitute for Luton in their 1-1 draw against Crewe while Tom Heardman came from the bench in the dying seconds of Hartlepool's 1-1 draw with Crawley. OUT ON LOANSiem de Jong - PSV Eindhoven (season-long loan)
Tim Krul - Ajax (season-long loan)
Henri Saivet - Saint-Etienne (season-long loan)
Florian Thauvin - Marseille (season-long loan)
Kevin Mbabu - BSC Young Boys (season-long loan)
Emmanuel Riviere - Osasuna (season-long loan)
Ivan Toney - Shrewsbury Town (loan until January)
Macaulay Gillesphey - Carlisle United (loan until January)
Adam Armstrong - Barnsley (loan until January)
Jamie Sterry - Coventry City (loan until January)
Haris Vuckic - Bradford City (loan until January)
Sammy Ameobi - Bolton Wanderers (loan until January)
Kyle Cameron - Newport County (loan until January)
Alex Gilliead - Luton Town (loan until January)
Tom Heardman - Hartlepool United (loan until January)
Paul Woolston - Darlington (work experience loan)