Five minutes before half-time, McKee squandered a golden chance to put Linfield back in front after Daniel Finlayson tipped Miller's free-kick over the crossbar.
Linfield started the second half with renewed determination and missed a golden opportunity two minutes after the restart when Miller's pinpoint cross was headed over the crossbar by Graham.
Lee Bonis gave Rahne a golden chance to win the match and the Gibson Cup in the 77th minute.
Chris Shields, who was playing in defense due to Linfield's injury crisis, played an uncharacteristically loose backpass that was caught by Bonis, who moved forward but tried to hit the ball over the goalkeeper. He was stopped by Chris Johns.
Aaron Donnelly also saw a low shot go wide for the champions, who up to that point seemed content with a draw that all but sealed back-to-back titles.
Linfield brought on Jordan Stewart, who returned after a long injury spell, in an attempt to find a late winner.
Fellow forward Mackie came closest to scoring after deflecting Kirk Miller's free-kick goal, but his shot hit the outside of the post and went wide, bringing down Ferguson.
They continued to press hard but it was in vain as Larne extended their unbeaten run in the league to four games and a place at Inver Park in this season's Gibson Cup was all but certain.
