Jonathan Smith's close-range finish put the Glens ahead but Eoin Bradley slotted it to level on 35 minutes.
Glenavon dominated the second half and Joel Cooper fired over keeper Dwyane Nelson to make 2-1.
Gordon salvaged a point for the hosts, latching on to Eric Foley's pass and blasting in with two minutes left.
Both sides were coming off weekend defeats while it was Roy Coyle's second game in temporary charge of Glentoran after Alan Kernaghan's resignation.
The Glens suffered an early setback when striker Nacho Novo was forced off with an injury following an innocuous challenge.
Bradley wasted an early opening for Glenavon before Smith converted a cross from Alex Leu.
Poor defending allowed Bradley in to equalise from Andrew Doyle's ball into the box.
Glenavon pressed for a second goal before the break and they took a deserved lead on 51 minutes.
Rhys Marshall almost added a third by heading just over and a minute later it was 2-2 courtesy of Gordon.
Glenavon move up one spot to fifth while the Glens remain ninth.
Steven Gordon hammered home a late equaliser to earn managerless Glentoran a Premiership draw with the Lurgan Blues at the Oval on Tuesday night.