Fowler cruised to victory over Abdelmalek Rahou of Algeria, catching him early in the first and putting him on the canvas for a count.
Fellow GB Boxing member and middleweight Aston Brown followed suit with a hard-fought win over Korean Jaemin Jeong.
The same could not be said for two other GB Boxing members however as Joe Joyce was stopped in the first round of his first super heavyweight clash with Hamza Beguerni.
Jack Bateson lost a split decision to Costa Rican David Rodriguez in the light flyweight second round while fellow Home Nations fighters Aqeel Ahmed, Ross Henderson and Joseph Ham all also fell.
Wales' Ashley Williams remains in the light flyweight draw however after reaching the last 16 with victory over Sri Lanka Malith Muthukarage in an all-action contest.