The Swiss striker scored two goals in 10 first-half minutes to help Christian Streich's men get the better of a Hannover side who find themselves in freefall, and just four points above Freiburg at the turn of the year.
Their best player Leonardo Bittencourt did grab a late consolation, but that may not be enough to keep coach Mirko Slomka, the club's longest-serving coach, in a job going into 2014.
Hannover had the first chance of the game in the seventh minute when Leon Andreasen lifted his shot over the crossbar from the edge of the penalty area after Bittencourt squared the ball for him.
It was the first and last time Oliver Baumann's goal came under serious threat in the first half, however, as Freiburg took charge of matters.
Mehmedi gave them the lead in the 25th minute when he was put through on goal, still with some work to do.
He turned inside onto his right foot and placed a low shot past Ron Robert Zieler into the bottom left-hand corner, giving Freiburg a lead for the first time in 10 Bundesliga matches.
Ten minutes later, Mehmedi made it two, giving Freiburg a two-goal lead for the first time this season.
He diverted a volleyed shot from Jonathan Schmid past Zieler, wrong-footing the Hannover goalkeeper who was already heading towards the other corner of his goal.
Freiburg then built the barricades, desperate to preserve what would have been their third win of the season.
Oliver Baumann became busier by the minute as Hannover sought their second recovery in a week after coming from three down to draw 3-3 with Nurnberg last week.
Bittencourt was denied twice by the Freiburg number one, who was finally beaten in the last minute when Edgar Prib's cross was headed in by Bittencourt, but it was too little too late for Hannover, and possibly also for Slomka.