Die Mannschaft rounded off its FIFA World Cup qualifying campaign with a 4-1 victory over Armenia in November, and picked up where it left off against Gadi Brumer's side in Sinsheim.
Havertz gave it a 36th-minute lead with a smart near-post header, before Timo Werner's 22nd international goal on the stroke of half-time ensured Germany had a healthy advantage at the interval.
Hansi Flick's side was content to play out the second period at a more pedestrian pace, although there was late drama as Thomas Muller and Yonatan Cohen exchanged penalty misses.
Despite Germany's dominant start, it did not carve out a shot on target until the 29th minute when Ofir Marciano got down well to repel Havertz's effort, with Julian Draxler prodding the rebound into the side netting.
Ilkay Gundogan curled straight at Marciano from a promising position soon after, before the Israel goalkeeper raced off his line to deny a clean-through Havertz.
The Chelsea forward was not to be denied from David Raum's resulting corner, however, heading home his eighth international goal from inside the six-yard box.
The hosts doubled their advantage in first-half stoppage-time through an unmarked Werner steering in Gundogan's indirect free-kick at the near post.
Only a superb Marciano save denied Thilo Kehrer a third on the hour mark as Germany continued to dominate after the break.
Muller fluffed his lines from 12 yards in the 89th minute after Lukas Nmecha had been brought down inside the area, while Cohen saw his spot-kick saved by Kevin Trapp after he had been tripped by Nico Schlotterbeck.