Stage III of the Norwood procedure is also known as the Fontan procedure. It is performed between 18 months and four years of age. In this stage, both the right atrium and the inferior vena cava (the major vein that collects oxygen-poor blood from the lower part of the body) are connected to the pulmonary artery. Now the oxygen-poor blood from the upper and lower body flows directly to the lungs bypassing the heart completely. Meanwhile, oxygen-rich blood flow from the lungs will be diverted through the single functioning ventricle and pumped out to the body.

The resulting oxygen-rich blood circulating to the entire body will result in a normal, healthy skin tone. Depending upon the nature and severity of the heart defects, some children may be healthy enough after stage II that stage III is not necessary.

One variation of Stage III is known as the lateral tunnel Fontan, or a total cavopulmonary connection (TCPC). In this procedure, a patch (made of either synthetic materials or the patient's own tissue) is used to create a tunnel within the right atrium. The tunnel links two major veins, the superior vena cava and the inferior vena cava, and is then connected to the pulmonary artery. A slight variation of the lateral tunnel Fontan is the fenestrated Fontan. In this procedure, a hole is made in the tunnel. This hole allows for decompression of the blood into the right atrium when the pressure within the tunnel gets too high. Later, if the patient has stabilized, the hole can be closed with either a stitch or a cardiac catheterization procedure. Many of these holes will close on their own with time.