Niall Currie's men went close to taking the lead on 21 minutes when Steven McCullough's wicked corner fell kindly for Baris Altintop at the back post, but with the goal gaping, the defender somehow contrived to nod wide.
They continued to knock on the door with Odumosu palming away a fierce drive from Shay McCartan.
Curran then opened the scoring for the Reds just after the half-hour mark.
Shea Kearney's teasing cross from the right sparked chaos in the Ports' defence, with Eric McWoods unwittingly playing the perfect dummy into the path of Curran, who pounced to prod home from close range.
The jubilation was short-lived however, as Obhakhan silenced the Solitude crowd with a moment of magic just minutes later.
Latching onto McCullough's inviting cross, he delicately lifted the ball over Odumosu with the outside of his boot for his seventh league goal of the season.
Jim Magilton's charges then reclaimed the lead early in the second half as Curran turned provider, threading a needle-perfect pass to captain Hale, who rifled past Aaron McCarey at his near post.
Just as it seemed the home side would secure all three points, the Ports struck in the 79th minute.
Lee Chapman's cross caused havoc in the six-yard box, and under pressure from Josh Ukek, Odumosu missed his punch, allowing Ukek to roll the ball into the empty net.