Obiang twice fired wide in the last 10 minutes as the visitors piled on the pressure following Stefano Lucchini's red card for a professional foul on Gianluca Sansone.
The result meant Atlanta failed to nudge any further clear of the Serie A relegation zone while Sampdoria's hopes of a top 10 finish were hit by their second game without a win.
The hosts looked more impressive from the start with Giacomo Bonaventura firing just over the bar with a free-kick in the sixth minute.
And the same player had another chance 10 minutes later when he hit a rising shot in from the middle of the box which fired just over the bar.
But as the half progressed the visitors began to press and Atalanta goalkeeper Andrea Consigli became increasingly busy, saving well from Daniele Gastaldello just past the half-hour mark.
Consigli's counterpart Sergio Romero kept Sampdoria level three minutes before the break with a superb save to stop a Gustavo Denis header from Cristian Raimondi's cross.
Nenad Krsticic fired a free-kick just over the bar for Sampdoria early in the second period, before Citadin Eder worked his way into the box and struck a low shot which was well saved by Consigli.
Bonaventura forced another fine save out of Romero at the other end before Lucchini's red card effectively ended the hosts' hopes of claiming all the points.
Obiang almost set up the opener two minutes later when he crossed for Mauro Icardi, whose header beat Consigli but hit the post.
And two minutes from time Obiang came close himself with a fierce drive which took a deflection and flashed inches wide with Consigli again well beaten.