The hosts had surprisingly moved ahead when Naldo met Kevin De Bruyne's teasing cross, yet the visitors levelled when a goalmouth scramble fell to Shaqiri, whose shot just crossed the line.
Bayern stepped up a gear with five second-half goals, the first coming when Thiago Alcantara's sublime pass was collected by Muller who tapped home after rounding the goalkeeper.
Mandzukic then notched against his former side for his 50th Bundesliga goal, before Ribery – making his first Bayern appearance since February 2 - and Muller's second helped Bayern make it 49 league matches without defeat.
Croatia international Mandzukic grabbed a second of his own to complete the rout as Bayern prepared for Tuesday's UEFA Champions League visit of Arsenal in fine style.
Bayern dominated possession in the early stages, and a swift counter-attack on 15 minutes saw Toni Kroos slip Shaqiri through on goal, but the Switzerland international could only hit tamely at Diego Benaglio as he struggled to keep his balance.
Wolfsburg had been largely untroubled, however, and the hosts moved ahead on 17 minutes. De Bruyne's out-swinging cross from the left was side-footed home by the stretching Naldo at the back post.
However, the hosts' lead would last just nine minutes as Bayern equalised in uncharacteristically scrappy fashion.
A corner from the left was not dealt with at all by the home defence, with Dante and Rafinha having shots cleared off the line before Benaglio was finally beaten as Shaqiri's effort sneaked in.
Shortly before the half-hour mark Benaglio had to be alert to parry Shaqiri's fierce half-volley as Bayern cranked up the pressure, while Robben flashed wide from the edge of the box.
Yet it was Wolfsburg who should have gone into the break ahead as De Bruyne side-footed weakly at Manuel Neuer when in a great position in the box.
Bayern once more stepped up a notch after the break, and a smart dinked free-kick from Thiago led to Robben lashing a volley over the crossbar.
Wolfsburg almost caught Bayern off guard on the hour mark, when Ivan Perisic dragged wide from the edge of the box.
That miss would prove costly just three minutes later. Thiago's intricate slide-rule throughball was collected by Muller who calmly rounded the goalkeeper and turned home.
And the game was put to bed on 66 minutes as Mandzukic - who had replaced Kroos – swept in Rafinha's cross from the right.
Ribery then got in on the act, smashing home Robben's pass after the Dutchman appeared to take the initial effort too far.
Bayern's second-half dominance continued in the 78th minute, Robben's pin-point cross was hammered home by the head of Muller and the Germany attacker played a part in the sixth, sliding into the path of Mandzukic who could not miss from six yards out.
Despite conceding six goals for a second-consecutive week, Wolfsburg remain in fifth place, while Bayern went 23 points clear at the top.
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