Adam took advantage of some poor goalkeeping from Andy McNeil to score a goal in each half from his set-pieces in a thrilling encounter.
Guillaume Beuzelin was red carded for Hibs in injury-time for denying Kris Boyd a goalscoring opportunity.
Hibs threatened first and Ross Chisholm saw a shot deflected over when Dean Shiels picked him out at the edge of the area from a corner.
Chisholm was then instrumental in Hibs' most flowing move of the first half.
He started it deep in his own half and ended up finding Steven Whittaker at the back post but he sent his shot over the crossbar.
Hibs moved in front after 20 minutes. Steven Fletcher caught Brahim Hemdani in possession 20 yards out before exchanging passes with Abdessalam Benjelloun and drilling an angled left-foot shot past Allan McGregor.
The striker was let down by his control a couple of minutes later when Kevin McCann set him up but the ball rolled away from him.
Rangers equalised after 23 minutes when Hibs goalkeeper McNeil misjudged a free-kick from Adam and the ball slipped into the net.
Barry Ferguson had a chance to put Rangers in front on the stroke of half-time after Boyd headed the ball down but he swiped his shot wide.
McCann scored at the other end in first-half injury-time when his wonderful 25-yard strike beat McGregor with the aid of a deflection.
Benjelloun should have done better then screw his shot wide three minutes into the second half after a slip by Ugo Ehiogu.
Rangers took full advantage and equalised shortly afterwards. Nacho Novo put Alan Hutton in the clear and he calmly lifted the ball over the advancing McNeil.
Hibs were back in front after 62 minutes when the Whittaker rifled in an unstoppable 18-yard shot after sloppy work by the Rangers defence.
But Adam produced another free-kick to catch McNeil at his near post and level the scores after 78 minutes.
Then came Beuzelin's late red card but Hibs held on for the point.