By Dan King - Newcastle United Digital Editor
Former Newcastle youngster Bradden Inman gave Crewe the lead at the New York Stadium before Kieran Agard equalised.
But Kelvin Mellor put the Railwaymen ahead once more and Vuckic was substituted after 61 minutes.
Lee Frecklington made it 2-2 from the penalty spot and, after Crewe had a spot-kick saved at the other end by Adam Collin, another United old boy, Alex Revell and Frecklington scored to give the Millers the win with Tavernier playing the whole game.
In the Scottish Premier League, Conor Newton and Adam Campbell couldn't prevent St. Mirren from slipping to a 2-0 loss at St. Johnstone.
Newton completed another 90 minutes after extending his loan deal during the week, while Campbell was withdrawn after 54 minutes.
Mehdi Abeid came off 30 minutes into Panathinaikos' 1-0 win over city rivals Panionios.