Vidal ghosted in at the back post to head home Joshua Kimmich's cross after 20 minutes at the Commerzbank-Arena to continue his goalscoring streak, ultimately ensuring Bayern will top the table at Christmas for a record 23rd year.
The Chile international's day ended early, though, as he was substituted after 55 minutes, Vidal having avoided a second booking moments earlier for a foul on Marius Wolf.
Vidal's match-winning header was Bayern's only effort on target in the opening half, and with Robert Lewandowski confined to a cameo role they continued to struggle after the restart.
Frankfurt had the better of the second period but like their illustrious visitors they offered little in the final third and failed to stretch Tom Starke on his first outing since coming out of retirement after Manuel Neuer's foot injury in September.
The hosts were briefly reduced to 10 men when Wolf was sent off after 73 minutes but the decision was changed to a yellow after consultation with VAR.
It did not do Frankfurt any good, though, as Bayern extended their lead at the summit to eight points.
Having made five changes from their win over Paris Saint-Germain on Tuesday, Bayern were forced into another before kick-off as Sven Ulreich suffered an adductor problem in the warm-up.
That gave veteran Starke his 100th Bundesliga appearance, and he made a confidence-boosting early save to deny Ante Rebic.
As the snow came down Frankfurt employed a high-pressing game but when they slacked off after 20 minutes Bayern capitalised.
A poor headed clearance from a right-wing corner dropped back to Kimmich and, with no challenge forthcoming, the full-back floated a sublime cross to the back post for Vidal to nod in.
Kimmich – featuring for Bayern for the 100th time – was proving a thorn in Frankfurt's side and another surging run led to Kingsley Coman lashing just wide.
With half-time approaching Starke ensured Bayern's lead remained intact with a routine save from Jetro Willems, Frankfurt having fashioned the chance for the wing-back with a training-ground free-kick routine.
A lazy Vidal challenge on Wolf enraged the home fans eight minutes after the restart but referee Harm Osmers opted not to show a second yellow card.
The demand for a red card was met 17 minutes from time but Wolf was the recipient after a clumsy challenge from behind on James Rodriguez.
However, Osmers consulted the video technology and reversed his decision, giving the winger a reprieve.
Even the introduction of leading goalscorer Lewandowski failed to produce a second goal for the visitors, but it mattered little as they secured a hard-earned three points to capitalise on RB Leipzig's draw at home to Mainz.
