THE Reds might have taken a sixth minute lead after Andy Coleman kept out a Marty Donnelly effort with his legs while Chris Scannell put the rebound wide.
At the other end on 13 minutes Diarmuid O'Carroll could only look on in frustration as his overhead kick was pushed onto the crossbar by John Connolly.
Chris Scannell opened the scoring for Cliftonville on 27 minutes when he slotted home from a Marty Donnelly pass across the box.
Glenavon almost levelled on 54 minutes when a Kyle Neill near post header drifted across the face of goal before going out wide.
But Cliftonville added a second four minutes later after Stephen Garrett rose highest from around 12 yards out to send a looping header past Coleman after Aaron Smyth had sent the ball over.
The Lurgan Blues pulled a goal back on 61 minutes after Smyth had upended David Magee just inside the box with O'Carroll converting from the spot.
Cliftonville were then reduced to ten men on 78 minutes after Smyth collected his second booking of the game for a foul on Davy Magee.
However, Marty Quinn's side were unable to make the most of their numerical advantage and so Cliftonville take their place in the last four.
Glenavon: Coleman, Shannon, Neill, Jay Magee, Harpur, O'Carroll, Kelbie, D. Magee, Hagan, Turkington, Graham subs Davidson (replaced O'Carroll 89), O'Hare (not used), Carson (replaced Shannon 83), Finlay (replaced Graham 77), McGonnell (not used)
Cliftonville: Connolly, R. Scannell, Johnston, Holland, Donaghy, Caldwell, McMullan, C. Scannell, Garrett, M. Donnelly, Smyth subs R. Donnelly (replaced M. Donnelly 61), Convery (not used), Templeton (not used), Gormley (replaced C. Scannell 80), Stuart (not used)
- Ciaran Donaghy gives chase as Kevin Kelbie sets off (Picture: PressEye.com)