The Blues opened lively when a cross on the edge of the box by Benas Vaivada met Rob Harvey but was headed narrowly wide of the right post.
Just minutes later, Vaivada was the orchestrator of a powerful cross from a free kick that was inches ahead of Tom Anderson.
A tangle of the feet of Ware goalkeeper Ethan Gannon in front of goal was exploited by Danny Ogunleye and set up for Mekhi McKenzie. But his strike was denied by the Ware defence.
The Blues continued to pose a threat goal-wards with an acrobatic bicycle kick from Harvey that was hit over the crossbar and a strike from Anderson which forced a save from Gannon.
In the closing stages of the first half, deadlock was broken when the fancy footwork of Harvey cut inside his marker before providing a cross into the box which was fired into the net by Shad Ngandu.
The second half saw The Blues take a more defensive approach and substitutions across the field were made. A through ball to McKenzie looked promising as he passed Gannon, but his shot was slightly wide of the right post, as was a shot from Jon Nzengo on the edge of the box.
A win today advances The Blues into next the qualifying round of the Emirates FA Cup with information regarding fixtures to follow.
By Michaela Georgopoulos