Gary Hamilton’s side survived a tense last few minutes but they certainly deserved their 1-0 win at Mourneview Park.
The first chance fell to Linfield on five minutes with Ross Clarke picking out Aaron Burns in the centre but he guided his header high and wide.
After Burns shot tamely at McGrath a long clearance into the Linfield half seemed to be covered by Niall Quinn but he fell over leaving Eoin Bradley in the clear and he ran on to smash a great shot past Jonathan Tuffey in the Linfield goal on 15 minutes.
Glenavon had the ball in the net again as Tuffey failed to get his hands to a cross but after Kevin Braniff swept the ball home the ref ruled it out for a push on the keeper.
Linfield as expected raised the tempo but McGrath was rarely troubled. The home side hit quickly on the counter but could not get a clean shot on goal.
On 35 minutes Linfield had a big shout for a penalty when Kris Lindsay moved in to challenge Burns but despite strong appeals referee Raymond Heatherington waved play on.
Three minutes before the break Waterworth got in behind to reach a long ball from Quinn but his angled drive flew wide of the Glenavon goal.
Glenavon made a change for the start of the second half with Ciaran Caldwell replacing Declan O’Brien as the visitors set about trying to find an early equaliser.
McGrath did well as he took the sting out of a shot on the turn by Waterworth as the home side found it hard to get out of their own half.
In a rare break Martyn put Bradley in the clear, he held off two defenders and pulled the ball back for Caldwell who dragged his shot wide.
Then at the other end Kris Lindsay did well to clear the loose ball off the line after Sammy Morrow and McGrath collided in the box.
The Lurgan Blues had a great chance to double their lead on 69 minutes when Patton broke clear and rolled the ball into the path of Bradley but after a touch his shot was pushed away for a corner by Tuffey.
As the minutes ticked away it became all very frantic as Linfield pressed for the equaliser. Patton had a chance to ease Glenavon towards the finishing line but his effort was blocked and then a volley from Martyn was deflected for a corner.
With three minutes to go Linfield were reduced to ten men after Ross Clarke picked up a second yellow for a late challenge on Marshall. Then Glenavon broke 4 on 1 but Braniff’s shot was saved and within seconds Waterworth broke into the box and hit a strong shot which McGrath did well to save.
Glenavon: McGrath, Kelly, Lindsay, Bradley, Patton, McGrory, O’Brien, Marshall, Braniff, Martyn, Singleton.
Subs: McKeown, Neill, Caldwell, Elebert, Lynch.