Carlos Quieroz's side are the highest-ranked AFC side in the FIFA rankings and they made that status tell as Al-Gharafa striker Taremi completed his double inside 25 minutes, either side of an own goal from erratic Yemen goalkeeper Saoud Al-Sowadi.
Iran's star man Sardar Azmoun got in on the act after half-time and substitute Saman Ghoddos drilled in a speculative long-ranger after 78 minutes as Team Melli established an early grip on proceedings in Group D.
Ahmed Al-Sarori lashed over a seventh minute chance for Yemen, who were initially indebted to Al-Sowadi for getting down brilliantly to his left to deny Taremi.
But the goalkeeper then undid his good work by spilling Azmoun's shot, with Taremi the beneficiary.
Al-Sowadi's evening got little better as Ashkan Dejagah's 23rd-minute free-kick hit the post and went in off his back, while he had no chance when Taremi headed gleefully home from Ramin Rezaeian's searching cross.
Iran should have finished the half with 10 men but Majid Hosseini's horrible two-footed lunge on Emad Mansoor Tawfik went remarkably unpunished.
Al-Sowadi's mixed outing continued as he twice denied Azmoun early in the second half – the initial save a superb reaction stop from another teasing Rezaeian delivery.
Predictably, Yemen's keeper was involved when the Rubin Kazan forward finally got on the scoresheet as he botched a routine punch.
Azmoun side-footed against the crossbar before Amiens midfielder Ghoddos completed the scoring and Mahdi Torabi rattled Al-Sowadi's furniture in stoppage time.
Vietnam are up next for Iran on Saturday, while Yemen will seek to bounce back against Iraq.