The midfielder's first-half strike and a late own goal were enough to secure all three points against a dangerous home side despite Pep Guardiola's significant list of injuriesBayern Munich as they won 2-0 at Hoffenheim on Saturday.
A tumultuous week for the German champions saw a 3-1 defeat to Porto leave their European hopes hanging in the balance, while the loss also saw long-serving team doctor Hans-Wilhelm Muller Wohlfahrt quit after being blamed for events in Portugal.
However, victory at the Rhein-Neckar Arena will go some way to lifting the mood for Pep Guardiola's men, who are now two wins away from securing a third straight domestic title.
The visitors took the lead through Rode, who marked his return to the starting line-up with a cool curling effort after good work from Robert Lewandowski inside the area.
Home captain Andreas Beck scored a last-minute own goal to seal the result after Bayern had kept pressure on the Hoffenheim goal with little reward.
An injury to Juan Bernat was the biggest blight in an ultimately successful 90 minutes for Bayern, who now host Porto in midweek hoping to rescue their continental campaign.
Again missing the attacking flair of Arjen Robben and Franck Ribery, Bayern struggled initially and saw Anthony Modeste go close twice for Hoffenheim, looping a header over before Manuel Neuer stood firm to deny the Frenchman one-on-one after sloppy play from Dante.
Finally forced into life by that scare, Bayern went ahead.
Lewandowski kept play alive after Muller had been denied and fed Rode, who shifted the ball onto his right foot and beat Baumann from 15 yards.
Rode nearly turned from hero to villain just before the break, appearing to trip Eugen Polanski inside the area, only for referee Tobias Stieler to wave away the home side's penalty appeals.
Bayern were dealt another injury blow shortly after the break when Bernat limped off with an apparent ankle problem.
Lewandowski snapped a looping effort onto the top of the bar two minutes into the half, before a fine double save from Baumann denied first Thiago and then Muller from close range.
Kevin Volland fired a volley just wide from distance moments later, but the hosts rarely looked like threatening Bayern's lead, with Sebastian Rudy bending a free-kick just wide five minutes from time.
Bayern's win was sealed in the last minute of stoppage time as Muller raced down the right before producing a driven cross into the area that Beck could only turn into his own net.
An identical scoreline against Porto on Tuesday will see Bayern through to the Champions league semi-finals, but they will likely require a more incisive showing up front if they are to overcome the Portuguese side.