Lars Bender slotted in from close range after Simon Rolfes headed the ball into his path in the 15th minute and Spanish defender Daniel Carvajal completed a move he started for his maiden Bundesliga goal seven minutes before the break.
Leverkusen, who have lost just one of their last 10 matches, move up to 24 points, as many as third-placed Schalke 04 and Eintracht Frankfurt and one behind champions Borussia Dortmund, who are second. Bayern, who crushed Hannover 96 5-0 on Saturday, are nine points clear.
Hoffenheim, who battled back in the second half and cut the deficit on the hour with defender Fabian Johnson's shot, slipped down to the relegation playoff spot with just one win in eight matches, piling more pressure on embattled coach Markus Babbel.
Jan Rosenthal fired in from 18 metres midway through the first half and defender Pavel Krmas took advantage of keeper Sven Ulreich's poor clearance to score his first goal of the season in the 67th.
Max Kruse notched his fourth goal of the season six minutes later, slipping the ball through Ulreich's leg with Stuttgart's defence reeling.
