In front of 8500 in Bremen, Hertha defender Peter Pekarik and Belgian-born winger Dodi Lukebakio scored quick-fire goals at the end of the first half to leave Werder 2-0 down at the break and the hosts were whistled off the pitch by their own fans.
Colombia striker Cordoba, signed from Cologne in mid-week, came on to start the move which Brazil Under-23 forward Matheus Cunha finished as Hertha went 3-0 up with an hour gone.
Davie Selke scored Bremen's second-half consolation goal before Cordoba capped his debut by tucking home Hertha's fourth goal on 90 minutes.
Just like Bayern, Cologne also had to play behind closed doors because of a rising rate of coronavirus infections for its 3-2 home defeat to Hoffenheim, for which Andrej Kramaric scored a hat-trick.
The Croatia striker put the visitors ahead after three minutes – capitalising on a mix-up in defence – netted a penalty and smashed home the winning goal in stoppage-time after Cologne had launched a late fightback.
In the capital, playmaker Michael Gregoritsch and winger Andre Hahn scored late goals as Augsburg beat hosts Union Berlin 3-1 in front of 4600 fans.
Newly-promoted Arminia Bielefeld earned a point with a 1-1 draw at Eintracht Frankfurt on its return to the top flight in front of 6500.
Stuttgart, which also came up, gave Freiburg a scare with late goals by Sasa Kalajdzic and Silas Wamangituka as it fought back in a 3-2 defeat in front of 8000.