By Anthony Marshall - Newcastle United Managing Editor
The Millers fought back from two goals down against Leyton Orient to force the game to a penalty shoot-out, in which they triumphed 4-3 from the spot.
And both United loanees played their part in Rotherham's famous victory, which made it back-to-back promotions for Steve Evans' men.
Tavernier started the game at right-back and threatened twice from distance early on, before Moses Odubajo and Dean Cox struck Orient into a commanding half-time advantage.
A tactical switch saw Tavernier pushed into a wide midfield role, where he continued to catch the eye and sent a free-kick onto the roof of the net. Then forward Alex Revell took centre-stage, scoring twice in five minutes, to get Rotherham back on terms.
Vuckic was introduced for Revell in extra-time, but the sides could not be separated and the contest was decided from the spot.
Tavernier confidently scored his penalty - along with three of his teammates - and goalkeeper Adam Collin made two stops to secure the Millers' place in the second tier.