The draw left Mohamed Amer's team in 12th place on 33 points, four points off the relegation zone. Zamalek remain sixth on 39.
Asyut were largely helped by Ghazl Mahalla's 1-0 defeat at Masri to secure their top-flight spot for the second season running.
Ibrahim Al-Helali's goal in Port-Saied left Mahalla in 13th place with 30 points, just above Telecom Egypt, who lost 1-0 to Ismaili.
Telecom, who are third from bottom on 29 points, will now vie with Mahalla for survival in the final week. Olympic and Tersana are already demoted.
At Petrosport Stadium, Arab Contractors grabbed a 2-2 draw to ensure their stay in the Premier division as well.
Ihab Al-Masri scored twice for the Mountain Wolves, whereas Ahmed Al-Mohammadi and Adel Mostafa got ENPPI's goals.
Elsewhere, Petrojet failed to enhance their fifth position after they drew 1-1 with Tersana in Cairo. Eric Bekoe's strike cancelled out Ahed Abdul-Magid's opener for the Hammers.
Gaish were the best movers this week as they jumped into the top half of the table with a 2-1 win over Olympic.
Goals from Hossam Abdul-Aal and Abdul-Sattar Sabri helped Farouk Gaafar's side move to seventh place on 38 points. Mahmoud Al-Attar scored Olympic's only goal.
Gaish face Ahli next week in a must-win game for the league holders.