RB Leipzig's shock 2-1 defeat at relegation-threatened FC Koln earlier in the day gave Hansi Flick's side the opportunity to go 10 points clear with four matches remaining.
Bayern did so with the minimum of fuss after Choupo-Moting – again deputising for the injury Robert Lewandowski – opened the scoring in the seventh minute.
A superb second from Kimmich made a response from Leverkusen deeply unlikely, as its struggles during the second half of this season were again laid bare at the Allianz Arena. Hannes Wolf's side is seven points behind four-placed Wolfsburg having played a game more.
Former Schalke and Stoke City forward Choupo-Moting has been much maligned during his stints at Paris Saint-Germain and Bayern, but the striker now has four goals in his past five appearances and smashed home from close range via a deflection off Sven Bender after Thomas Muller's effort was saved.
Once again, Kimmich oozed class in midfield and Leverkusen goalkeeper Lukas Hradecky had no chance when the Germany international let fly form the edge of the box in the 13th minute.
Patrik Schick darted in behind Bayern's high line but could only entertain Manuel Neuer with a routine save, while Hradecky fumbled at the other end when Kimmich tried his luck again.
Leverkusen's number one sharply denied David Alaba before the break but Choupo-Moting rolled a clever finish past him in the 65th minute, only to be denied by a marginal offside call.
Leroy Sane, introduced from the bench with a point to prove, lashed over with 20 minutes remaining.
Another flying winger, Leon Bailey, almost helped to bring Leverkusen back into the contest when his cross was hit into the turf and against the crossbar by substitute Karim Bellarabi.
That prompted something approaching a rally from the visitor, although not one to sufficiently discomfort Bayern as it cantered towards the finish line and another domestic title.