The win takes Leverkusen up to fifth, level on points with fourth-placed Borussia Moenchengladbach who have a game in hand.
German international Havertz, widely linked with a possible move to Premier League leaders Liverpool at the end of the season, assisted one goal and created several other chances.
Augsburg went close in the opening stages, with Florian Niederlechner heading just wide in the 18th minute.
It was Leverkusen however who would score first, with Moussa Diaby taking advantage of an excellent Havertz assist in the 25th minute to score his third goal of 2020.
From there on, Leverkusen took the initiative, dominating possession and territory.
They almost doubled their lead in the 53rd minute after another expert pass from Havertz put the ball on a platter for Mitchell Weiser, but the former Bayern winger was unable to control it.
The hosts did not have to wait long to get on the scoresheet again, however, with Nadiem Amiri scoring a stunning solo goal to make it two.
After gathering possession in the Augsburg half, Amiri ran past several defenders before firing the ball into the bottom corner of the net to chalk up his first goal for Leverkusen.
Havertz was substituted in the 84th minute to rapturous applause.
Later on Sunday, Wolfsburg welcome Mainz to the Volkswagen Arena hoping to keep their three-match unbeaten run going.
The final match of the round will take place later on Monday, when Union Berlin travel to Eintracht Frankfurt.