Torsten Lieberknecht's side only had 18 points on the board heading into Tuesday's match, but fine goals from Dominik Kumbela and Havard Nielsen refuelled their ambitions of securing a place in the top flight next season.
But Kumbela's third - and second of the night - was a sensational bicycle kick that was worthy of rubber-stamping the three points.
The clash in Braunschweig took fourth-rating on the Bundesliga card - but there was a substantial amount riding on the encounter.
Perhaps surprisingly considering the league standings - but not undeserved over 18 minutes - the hosts took the lead through captain Kumbela who finished from close range.
The advantage lasted the best part of two minutes until sharp-shooter Muller tapped home Zdenek Pospech's cross-cum-shot from right-back.
But it was the basement boys who went into half-time holding the keys to the three points.
A scrappy set-piece was not cleared on several occasions by the normally ruthless Mainz defence.
Instead, Nielsen snatched at his shot which trundled through the hands of Loris Karius in the visiting goal and sneaked inside the post.
The second 45 minutes played out to Braunschweig's game plan with Mainz unable to carve open a compact home defence.
Even the introduction of Japanese international striker Shinji Okazaki from the bench came to nothing for Thomas Tuchel's men.
Yet the lack of scoring chances was fitting considering Kumbela's top class overhead kick finish on 74 minutes from 12 yards.