Havertz enhanced his reputation further amid talk over a big-money move to the Premier League by scoring twice in a 4-1 thumping of Werder Bremen last weekend when the Bundesliga resumed.
The 20-year-old starred again on Saturday, helping himself to a goal in each half as Leverkusen stretched its unbeaten run to 12 matches in all competitions.
Forward Havertz opened the scoring early on and struck again with a contentious penalty to take his tally for the season to 14 after Marcus Thuram equalised early in the second half.
Sven Bender's header made sure of the points for Peter Bosz's impressive side in a game played behind closed doors, with Gladbach supporters probably glad to it was cardboard cutouts rather than actual fans watching on from the stands.
Havertz wasted no time in making his mark, taking a nicely weighted pass from Karim Bellarabi and sliding home to round off a swift break and make Gladbach pay for giving the ball away cheaply just seven minutes in.
Breel Embolo was replaced by Lars Stindl after taking a kick on the leg before Yann Sommer spared Gladbach further pain when he denied the lively Bellarabi.
Lukas Hradecky had been little more than a spectator at the other end, but he breathed a sigh of relief after getting away with failing to hold a Florian Neuhaus drive five minutes before the break.
Leverkusen should have doubled its lead just prior to the interval, when Havertz's left-footed effort struck the crossbar and Kerem Demirbay's follow-up effort was blocked by Nico Elvedi with the goal gaping.
Thuram levelled seven minutes into the second with a clinical right-footed finish after he was played in by Alassane Plea and he ought to have put Leverkusen in front soon after too, but was thwarted by Hradecky after racing through.
It was Havertz who was celebrating a brace soon after, slotting just to Sommer's right from the spot after Elvedi was somewhat harshly adjudged to have fouled Bellarabi when he was in the process of firing wide.
Leverkusen had breathing space when Bender rose to node home Demirbay's free-kick nine minutes from time, with Plea and Oscar Wendt spurning late chances as Gladbach's UEFA Champions League hopes suffered a blow.