Lewandowski, sporting a new, peroxide-blond hairstyle, grabbed Bayern's second goal not long after Arturo Vidal's 31st minute opener and added another early in the second half, to take his league tally to 13 goals.
The Poland striker has now scored 18 times against Augsburg in 13 Bundesliga matches, more than against any other club.
"Obviously I am happy but to be honest I do not care against whom I score," Lewandowski told reporters.
"We struggled a bit with our movement at the start but after the first goal everything became easier. We showed we are in good form."
The Bavarians, who have not dropped a point since Heynckes took over from Carlo Ancelotti last month, are top on 29, six ahead of RB Leipzig who drew 2-2 at Bayer Leverkusen. It was also Heynckes' 500th Bundesliga win as coach and player, extending his own record.
Borussia Dortmund, Bundesliga leaders only a few weeks ago, are in complete free fall, having dropped to fourth on 20 after their 2-1 loss at VfB Stuttgart on Friday, their fourth league defeat in their last five matches. Borussia Moenchengladbach took over third place on 21 after Raffael struck twice in their 4-2 win at Hertha Berlin.
Augsburg were bold and matched Bayern for half an hour before Vidal turned and fired in from close range for the lead.
The Chilean then sent Lewandowski through with a defence-splitting pass to double it.
The Pole then volleyed in a perfect Joshua Kimmich cross four minutes after the restart to knock their opponents out in a perfect dress rehearsal for their Champions League match at Anderlecht next week.
Leverkusen proved too hard to crack for Leipzig as they came from a goal down twice to earn a point, with Kevin Volland netting the final equaliser in the 74th minute. Leverkusen played most of the second half with 10 men after the dismissal of Benjamin Henrichs.
VfL Wolfsburg notched their first win under coach Martin Schmidt following seven successive draws, beating Freiburg 3-1 to climb to 13th.
Hoffenheim missed their chance to go third, needing a stoppage-time equaliser through Mark Uth to rescue a 1-1 draw against Eintracht Frankfurt and are fifth on 20.
(Reporting by Karolos Grohmann; Editing by Christian Radnedge)
