Why does hypertension occur in obstructive sleep apnea?
From Obstructive sleep apnea syndrome and hypertension: mechanism of the linkage and 24-h blood pressure control:


  OSAS directly induces negative intrathoracic pressure and decreases pulmonary stretch receptor stimulation, chemoreceptor stimulation, hypoxemia, hypercapnia and microarousal. These changes potentiate various risk factors, including the sympathetic nervous system, renin-angiotensin-aldosterone system and inflammation.




Summary:


Low oxygen levels at night increase oxidative stress to the body inducing inflammatory reactions and damage to the interior of blood vessels
Nitrogen monoxide production is decreased, decreasing flow-mediated dilation of blood vessels
Frequent night-time awakenings bring elevated sympathetic nervous system activity
During episodes of hypoxia, blood pressure and heart rate increase
"Increased sympathetic nervous activity may also cause coronary spasm and induce vasospastic angina pectoris."
"[P]eriodic negative intrathoracic pressure (−80 mm Hg, at most), together with a midnight surge of BP, exerts mechanical stress on the ventricular and atrial walls, resulting in the development of left ventricular hypertrophy and left atrial remodeling and, consequently, an elevated risk of heart failure and atrial fibrillation"