The 20-year-old nodded Leverkusen into a 28th-minute lead at the Weserstadion but Bremen levelled quickly through Theodor Gebre Selassie.
Havertz restored Leverkusen's advantage with another header.
Heading into the new week like pic.twitter.com/JakL83Ad3W
— Kai Havertz (@kaihavertz29) May 18, 2020
Peter Bosz's side wrapped up the victory with second-half goals from Mitchell Weiser and Kerem Demirbay.
Leverkusen have 50 points after 26 games while RB Leipzig have 51 following a surprise 1-1 draw on Saturday withFreiburg.
Bayern quest
Bayern Munich, seeking their seventh consecutive championship and a record-extending 29th overall, set the pace with 58 points. Borussia Dortmund are second with 54 and Borussia Moenchengladbach are third with 52 points.
The Bundesliga resumed on Saturday after a two-month suspension while the German government attempted to stem the spread of the coronavirus pandemic which has left 8,000 people dead in the country.
League authorities in the Netherlands, Belgium, Scotland and France have terminated their seasons due to the disease.
In France, Amiens, who were relegated when the Ligue de Football Professionnel ended the campaign, have started legal action against the decision.
Strict rules for return
Training regimes have been stepped up in Spain and England as La Liga and the Premier League target restarts in June.
Portugal's Primeira Liga has set a target date and Italy’s Serie A says it is awaiting government approval for a return in June.
Like in Germany, the action throughout Europe will resume without fans in the stadiums and strict health protocols for the players and coaching staff.
While Leverkusen chase a place in the Champions League, European club football’s most prestigious competition, Bremen are locked in a battle for Bundesliga survival.
They are 17th in the 18 team division and five points from 16th - the slot for a relegation play-off with the third-placed team from the second tier.
