McKee wasted a good chance to put Linfield back in front five minutes before the break, blazing over the crossbar after Daniel Finlayson had knocked down Millar’s free-kick into his path.
Linfield started the second half with renewed intent and squandered another fine opportunity two minutes after the restart as Graham headed over the crossbar from Millar’s pin-point cross.
Lee Bonis had a fine opportunity to win the game and the Gibson Cup for Larne on 77 minutes.
Chris Shields, who was playing in defence due to Linfield’s injury crisis, uncharacteristically played a loose back pass which Bonis latched on to and he drove forward before being thwarted by Chris Johns in his attempt to loft the ball over the goalkeeper.
Aaron Donnelly also saw a low shot drift wide for the champions, who had until that point appeared content to settle for the draw which would all but secure back-to-back titles.
Linfield brought on the returning Jordan Stewart, returning after a long injury lay-off in their attempt to find a late winner.
It was fellow forward McKee who went closest to scoring, as he diverted Kirk Millar’s free-kick goal wards, but it hit the outside of the post and went wide, with Ferguson beaten.
They continued to press hard, but to no avail as Larne extended their unbeaten run in the league to four games and all but ensured the Gibson Cup will stay at Inver Park this season.