Coleraine gained revenge for an earlier defeat by Omagh Academy in a hard-fought cup tie at Ballycairn Road.
But their injury crisis increased when wing-forward Ollie McDowell broke his leg in the second half.
Coleraine coach Richard Beggs was saddened by the injury to McDowell.
He added: “We have been blighted by injuries all season and now Ollie McDowell is out.
“I never thought we got out of third gear and as a performance I would give it seven out of 10.
“We had a few excellent players. Conor Shiels was magnificent at out-half and Peter Kidd at scrum-half, with an eye for a break, was the ideal link. Danny McAlister and Mark Gordon were also evident and I feel our performance, overall, warranted a win.
“Omagh made it very difficult for us and it should have been easier.”
Ross Hunter felt Omagh's effort was error-strewn.
“We started off well but were unable to convert possession into points. They had a good try but we had our chances and can take a lot from the game,” he said.
“Scott Hemphill and Adam Stevenson in the centre were called upon to defend and they also played well in attack. Tight head prop James Kelso held his own and Stuart Allen was dominant in the line-out.
“We came close but, on another day, we could well have won.”
After Omagh missed an early penalty the home team took the lead when Conor Shiels’ penalty bounced off the post and after a few phases right winger Peter Acheson crossed in the corner.
Shiels made it 8-0 with a drop goal and although Omagh fought back with attack after attack the defensive work of Mark Gordon and McDowell kept Coleraine’s line intact in the first half.
Four minutes after the restart Coleraine went further ahead with a brilliant try.
Following a ruck, the ball came back to full-back Bradley Dempster who broke through and linked with Johnny Crowe. The centre made ground but Dempster was alongside and popped the ball up to prop Danny McAlister who scored.
Following the injury to McDowell, Omagh were encamped on the Coleraine line and and were eventually rewarded when James Catterson dived over for Lloyd Kane to goal.
From the drop-out, though, Logan, who had moved to No 8, picked up to make the score 18-7 before Omagh winger Dean Henderson went over near the end.