Sampdoria gradually improved as the game wore on and Okaka saw his header cleared off the line, with Muriel sending an overhead kick wide of the post moments later.
They finally made their pressure pay in the 68th minute when Okaka chipped a ball over the top for Muriel, who controlled on his chest before crashing a half-volley into the net.
Within minutes, German Denis had a golden opportunity to score for the hosts, but his close-range attempt was beaten away by Emiliano Viviano.
Atalanta were made to pay for that miss with nine minutes left to play as Eto'o's shot was spilled by Sportiello, and Okaka followed up to slot in the rebound and give his side the lead for the first time.
It proved to be the winning goal, as Sampdoria held on to win for the first time in six league outings and move up to sixth place in the Serie A table.