Taremi pounced on some uncertain defending to score what looked like being a scrappy opener, only for a lengthy VAR check to disallow it out for a handball infringement.
The visitor went close earlier in the half through an Otavio cross that came back off the frame of the goal, prompting Diego Simeone to introduce Antoine Griezmann from the bench.
But despite having the likes of Griezmann, Luis Suarez and Angel Correa on the field, Atletico could not find a trademark late goal – even after a late Chancel Mbemba red card – as they kicked off their Group B campaign with a draw.
Suarez was denied by Diogo Costa inside the opening six minutes when taking on an early shot, but that proved to be the home side's only serious attempt in the first half.
Porto did not fare much better before the interval as Taremi screwed wide from a good position and Marko Grujic headed over from the best of their opportunities.
Atleti was given a scare when Otavio's attempted cross looped over Jan Oblak and hit the post, with the loose ball just out of Taremi's reach.
Simeone turned to Griezmann and Correa at that point and the latter got an angled drive on target soon after that Costa was equal to down low.
The host had scored late goals in their last two matches but it was Porto who went closest to snatching all three points here through Taremi.
However, the ball ricocheted off the forward's hand on its way over the line and was chalked off, and further misery was to come for Porto when Mbemba saw red for bringing down Griezmann in added time.