The game endured a slow and turgid start as the action was broken up by several offside calls and heavy challenges.
Just when it looked like the game would reach the halfway point as a stalemate, Anthony Ujah laid the ball off to Junuzovic, who drilled home from close range to put the visitors into the lead.
Hoffenheim were level five minutes after the restart, however, as Mark Uth slipped the ball to Eduardo Vargas on the edge of the box, with the former Queens Park Rangers man rifling low into the middle of the net.
The second half proved much livelier than the first period, with Kevin Volland collecting a tailored ball and firing a ferocious shot from the edge of the box, but Felix Wiedwald pulled off an acrobatic save to stop the danger.
In the second minute of injury time, the visitors surged back into the lead when Ujah collected Claudio Pizarro's pass and lashed home, and just two more minutes elapsed before Junuzovic claimed his second of the game to confirm victory for Bremen.