Frankfurt dominated proceedings from start to finish against a Bremen side who spent much of the game with 10 men after Franco Di Santo saw red.
They were already behind at that point with Vaclav Kadlec scoring the first of his two goals before Aaron Hunt missed a penalty for the hosts, and an own goal from Sebastian Prodl summed up their day.
When Takashi Inui is in this kind of form, you know you are in for a busy afternoon and the Japanese winger was flying, causing problems each time he received the ball.
His pass set up Bastian Oczipka to cross from the left and Kadlec met the ball from close range, lifting it into the top corner to put the Eagles in front in the 14th minute.
That was not enough for Armin Veh's men and Tranquillo Barnetta twice went close to doubling their advantage before Cedrick Makiadi almost levelled at the other end with a header against the post.
Bremen were reduced to 10 men in the 26th minute when Di Santo was shown a red card after leaving Oczipka needing stitches to a face wound with a dangerous tackle.
Some of the fans tried to lift their team in a difficult moment while others started to send the first whistles around the Weser Stadion.
The dissenters gained the majority when Kadlec headed in Sebastian Jung's cross to make it two for the guests before the break.
Bremen had the chance to get back into the game early in the second half when Hunt earned a penalty, but he failed to convert from the spot.
The home team searched for a goal from open play, but when it arrived, it came at the other end with Prodl beating Kadlec to the ball, but sending it into his own goal to compound Bremen's woes in the 77th minute.