The Leicester captain struck after just seven minutes to seal victory for the Premier League new boys ahead of their return to the top flight following a 10-year absence.
The hosts were full value for their success at the King Power Stadium and manager Nigel Pearson will have been encouraged by the performance as Leicester completed their preparations for the new season, which they open against Everton next Saturday.
Bremen, meanwhile, will be hoping for a much improved display when they face Illertissen in the DFB-Pokal in eight days' time.
Leicester made a bright start to proceedings and were rewarded early on as centre-back Morgan glanced home Riyad Mahrez's right-wing corner.
Morgan had the ball in the net again in the 23rd minute, but he was denied a second by the referee, who disallowed the headed effort for a foul.
Just two minutes later Leicester were grateful to goalkeeper Kasper Schmeichel, the Dane preventing Bremen striker Nils Petersen from notching with a fine one-on-one save.
Schmeichel continued to frustrate Petersen in the first half, keeping the 25-year-old at bay with a triple save in the 31st minute.
Predictably changes arrived in the second half and Leicester substitute Leonardo Ulloa caused the visiting defence a number of problems in the second half.
The Argentinian - making his debut after joining from Championship outfit Brighton and Hove Albion - was twice denied by Bremen goalkeeper Raphael Wolf.
First the shot-stopper kept out an Ulloa header with his heel three minutes into the second half, before frustrating him again with a fine stop on from the 28-year-old's half-volley.
But, Wolf's heroics proved in vain as Leicester held firm to claim triumph.
