The Kenyan skipper, who recently signed for France side AC Ajaccio, scored a brace as AFC Leopards' Paul Were added the third for a comfortable win
This was the first match that Oliech was playing for Stars since signing for Ajaccio from ligue two side AJ Auxerre and the confidence in his play was evident. He netted a double and set up the third goal to inspire Stars to their first win since failing to go past Burundi in an Africa Nations Championships (Chan) match.
Oliech scored first in the 5th minute slotting home from the penalty spot after Humphrey Mieno had been brought down in the box. Then in the 16th minute, Oliech ran to slot home a David Gateri's splitting pass.
The Kenyans were in complete control in the entire first half with Celtic midfielder Victor Wanyama controlling matters in the center of the pitch.
Together with Gateri, who was playing his first match at the senior level, the duo kept their opponents subdued for a good chunk of the first half.
The Libyan opposition woke up only in the dying minutes of the first half and had two efforts at goal but Sali Abou's efforts both proved futile.
Oliech, who was arguably man of the match, ended the first half on a high after failing to beat the Libyan goalkeeper Mohammed Nashnoush in a one on one situation as the clock hit the 42nd minute mark.
On the stroke of half time, Oliech again found himself with only Nashnoush to beat but he lost control as the Libyan defence quickly recovered.
Stars started the second half strongly with strong forays into their opponents half. Once again the midfield was instrumental and Gateri just upped his game once more. Paul Were scored the winning goal in the 78th minute to ensure Stars kept victory and an improvement in their rankings.
There were several attempts by the Libyans to equalise but the Kenyan defence stayed firm. Hard fighting Abdalla Juma was momentarily removed from the pitch after suffering a slight injury but he was back in the match.
A delighted Football Kenya Federation (FKF) President Sam Nyamweya congratulated the team for the huge away win and promised they will do well against Nigeria in next month's World Cup qualifier.