Belgian defender Daniel van Buyten headed the hosts into the lead in the 58th minute and Mario Gomez doubled the score with his ninth goal of the season, slotting home from close range. Arjen Robben then curled in a free-kick four minutes from time.
Bayern, who have now won their last nine matches in all competitions, are on 42 points from 20 matches, one ahead of Bayer Leverkusen.
"This was our best home game so far," Bayern coach Louis van Gaal told reporters.
"We were superb when we had possession, we created many chances and scored beautiful goals. I saw an outstanding Bayern Munich today. I am satisfied," said the Dutchman.
Third-placed Schalke 04 kept up the pressure with a 2-0 win over Hoffenheim, to move level on 41 points with Leverkusen.
Schalke striker Kevin Kuranyi took his goal tally to 11 this season when he grabbed the lead on 19 minutes and Lukas Schmitz made it 2-0 four minutes after the restart with a deflected shot.
FRANTIC PACE
Bayern looked determined to extend their winning streak when they set a frantic early pace. Croatian Ivica Olic saw his sixth-minute header saved by keeper Heinz Mueller, who also denied Gomez a little later.
The hosts, with Dutch winger Robben reigning supreme on the right, squandered their biggest chance when Thomas Mueller was brought down in the box in the 32nd minute. Bayern keeper Hans-Joerg Butt took the penalty but was also denied by Mueller.
Heavy snowfall affected the quality of the match in the second half as both teams struggled on the slippery surface.
Bayern kept up the pressure though and got their deserved lead when Van Buyten rose high to connect with a Robben cross and keeper Mueller let the ball slip through his hands and legs.
Bastian Schweinsteiger rattled the bar with a powerful header before team mate Gomez sneaked in to slot home a Philipp Lahm cross from the right in the 75th.
Robben crowned yet another sparkling personal performance when he curled a free-kick past Mueller in the 86th for the 3-0.
Werder Bremen lost 4-3 to Borussia Moenchengladbach, who scored three times in the opening 18 minutes.
Coach Thomas Schaaf, whose team has not won in the league since late November, is under mounting pressure with Bremen now 14 points off the pace in sixth place.
Bottom-placed Hertha Berlin, battling to lift themselves out of the relegation zone, remained unbeaten for the third straight week, with a goalless draw against VfL Bochum.
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