However, the top seed recovered in the second with a back-fist strike and a hook kick making it 7-5.
The USA athlete tried closing the gap in the third and final round but could not work past his way Tazegul's defences.
Tazegul said: 'I am happy that I won but I cannot relax now. It is too early to celebrate.
'At the Olympics, every opponent is tough. I know that I will face tougher competitions in the rounds to come.
'I am a fighter. I hope I can make it to the final for the gold.'
New Zealander Logan Campbell got knocked out of the preliminaries after losing to Ukrainian Hryhorii Husarov 10-6.
In the women's -57kg preliminaries, top seeded Tseng Li-Cheng from Chinese Taipei dominated her opponent Thai Rangsiya Nisaisom from the very beginning, winning the fight 4-1.
Fourth seeded British fighter Jade Jones scored an impressive win by overpowering her opponent, Dragana Gladovic from Serbia.
The young Brit was off to a slow start in the first round but soon came back to winning form, taking a huge lead of 14 points over her rival to prevail.