Cliftonville came from a goal down to secure a deserved three points and move into third place in the Premiership.
Ryan Harpur stabbed the ball in from six yards at the back post after meeting a Niall Henderson free-kick in the sixth minute.
Rory Donnelly provided the assist for Ryan Catney to slide the ball into the bottom corner from 10 yards on 60.
Chris Scannell took advantage of a defensive mistake to beat Davy O'Hare for his 12th of the season after 73.
After Glenavon scored their opener, John Connolly produced a fine save from Harpur.
Diarmuid O'Carroll skewed a shot wide and Donnelly saw his shot well saved by O'Hare.
For Tommy Breslin's in-form side, this was their eighth consecutive victory.