The Blues moved five points clear at the top of the Carling Premiership as Gary Hamilton lost his first match in charge of Glenavon.
Both sides wasted good first-half chances with Glenavon's Conor Walsh blazing over before Michael Carvill volleyed off-target from close range.
Albert Watson headed against the bar before Carvill finished at the near-post from Mark McAllister's cross.
Linfield were in control and McAllister was denied by keeper Davy O'Hara.
Hamilton was forced to make an early change when injured defender Cameron Grieve was replaced by Kyle Neill.
The Lurgan Blues held firm in a tight first half of few chances but the champions took a grip of affairs after the break.
Watson's effort against the woodwork was followed by a superb save by O'Hare to keep out Carvill's low shot.
Carvill made the breakthrough on 67 minutes to give the Blues a deserved lead.
Linfield pushed for a second goal and again O'Hare came to Glenavon's rescue, blocking McAllister's shot after the striker was sent clear.