First-half scores by striker Werner and an Omar Hawsawi own goal sealed the win as Germany were only rarely threatened by Saudi Arabia, who play hosts Russia in the opening World Cup match in Moscow on Thursday.
Werner was in the thick of the action for the 62 minutes he played of the friendly.
The scoreline flattered the Arabians, who converted a late penalty at the second attempt.
However, German hearts were in mouths in added time when only robust defending prevented Al-Sahlawi grabbing a shock equaliser.
"We conceded a few counters, the holes were too big, but we are a tournament team and we still have a week left - Germany shouldn't worry."
Having failed to win any of their previous five games, including a shock 2-1 defeat at neighbours Austria last Saturday, a full-strength German team dominated for long spells in Leverkusen.
Both Sami Khedira and Reus hit the post in the first half as Germany could easily have doubled their tally, but there were also worrying defensive lapses from the hosts.
Saudi Arabia were crushed 8-0 by Germany in a group phase game at the 2002 finals and it looked like a similar rout was on the cards early on.
Germany grabbed the lead after just eight minutes when a Joshua Kimmich long ball was beautifully controlled by Reus, who squared for Werner to fire home. Reus, who heart-breakingly missed the 2014 World Cup triumph after tearing ankle ligaments in the final warm-up match, then clattered the post three minutes later.
It took 30 minutes for the visitors to trouble the German defence when forward Fahad Al-Muwallad twice shot wide.
Khedira forced Saudi goalkeeper Abdullah Al-Mayouf into a reflex save on 37 minutes, palming his shot onto the post. The second goal came just before the half-time whistle when Werner's cross for Thomas Mueller was tapped into his own net by Hawsawi.
Ilkay Gundogan replaced Reus for the final 30 minutes and was booed by Germany fans, despite going close on 61 minutes.
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