Fans witnessed a quiet first half with a few chances by Eintracht Frankfurt while Ansgar Knauff's shot inside the near post was denied by Allan McGregor and Filip Kostic's volley went wide of the target.
Giovanni van Bronckhorst's side took a 1-0 lead when an Eintracht Frankfurt defender slipped and left Joe Aribo free to run in a one-on-one with the goalkeeper. It was easy for Aribo to beat Kevin Trapp to score the opener in the 57th minute.
Twelve minutes later, Eintracht Frankfurt responded with a goal by Rafael Santos Borre, who touched the ball between the two Rangers center-backs to defeat McGregor at his near post, sending the match into extra time.
Near the end of extra time, Trapp blocked Kent with an impressive save by his legs from six yards out to keep Frankfurt alive.
The match went into penalties.
Eintracht Frankfurt became the winner of the night after beating Rangers 5-4 on penalties.
The German side clinched their second European victory after lifting the UEFA Cup in 1980.
They also automatically qualified for the next season's Champions League.
More about: UEFA
