The Oluyole Warriors made a strong start at home and were rewarded in the 14th minute when Lucky Emmanuel fired them ahead.
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Inter Lagos quickly responded, with Adigun Damilare restoring parity nine minutes later after finishing a well-delivered ball into the box.
Shooting Stars regained the advantage just before half-time when Sodiq Ibrahim confidently converted from the penalty spot.
The visitors enjoyed a more balanced contest after the break, with both teams creating chances.
Shooting Stars were handed an opportunity to seal victory in stoppage time when they were awarded another penalty, but Mustapha Adams failed to convert.
The hosts nevertheless held firm to secure all three points and begin the new NPFL season positively.