Lewandowski, last season’s Bundesliga top scorer, has 24 league goals this campaign like Aubameyang, who scored for Borussia Dortmund in their 1-1 draw at Schalke in the 150th Ruhr Valley derby.
The Poland international has now scored 36 goals in all competitions for Bayern this season.
Lewandowski also proved he can provide goals by setting up Thomas Mueller for Bayern’s second, his backheel then let Thiago Alcantara stab home their fourth.
His opening strike was a trademark Lewandowski goal as Thiago’s pin-point pass put him behind the defence, with the Pole trapping the ball and curling home with his left foot on 17 minutes.
He then delivered the cross for Mueller to deservedly net only his third league goal of the season, after the Germany star twice hit the woodwork in the opening 36 minutes.
Lewandowski held off a defender to make it 3-0 on 55 minutes following Franck Ribery’s superb final pass, and his delightful backheel to Thiago gave the Spain midfielder a simple tap-in on 62 minutes.
The Poland star completed his hat-trick with a header on 79 minutes before Mueller grabbed his second a minute later before going off injured.
In Gelsenkirchen, Aubameyang kept pace with Lewandowski by netting his 24th goal in as many league games as he fired home Shinji Kagawa’s final pass on 53 minutes against Schalke.
Just as he did when scoring in the Ruhr derby in February 2015, the flamboyant Gabon striker, Dortmund’s self-styled ‘Batman’, donned a black mask to celebrate.
However, the hosts equalised when Thilo Kehrer, 20, slotted away his first Bundesliga goal in only his 12th game to the delight of the home fans.
Schalke were denied a penalty in the dying stages when the ball struck Dortmund defender Marc Bartra’s hands.
The decision so incensed Markus Weinzierl that the Schalke coach was sent to the stands as the draw left Dortmund fourth in the table with Schalke ninth.
After back-to-back defeats before the international break, second-placed RB Leipzig emphatically returned to winning ways with a 4-0 romp against bottom side Darmstadt, who had midfielder Sandro Sirigu sent off.
Guinea midfielder Naby Keita, who collapsed after last month’s shock 1-0 defeat to Wolfsburg, marked his return with two goals.
After Keita’s opener on 12 minutes, playmaker Emil Forsberg and captain Willi Orban both netted before Keita added the fourth with 10 minutes remaining.
Denmark midfielder Thomas Delaney netted a hat-trick for Werder Bremen in their 5-2 drubbing of Freiburg to lift them up to mid-table.
Hamburg climbed out the bottom three with a 2-1 victory at home to Cologne as Lewis Holtby netted the winner in the 92nd minute.