Pelicans had dropped to 14th after going five matches without a victory, but when Brett Stapley broke the deadlock after just 42 seconds, hopes of picking up their first points since 20th December would have been growing.
However, it took Lukko just over five minutes to quell those hopes and turn the match around - Aarne Intonen's incisive pass found Henri Ikonen in front of the net to equalise, then when Casimir Jurgens was penalised for holding, Alex Beaucage put the hosts in front with a powerplay goal.
With just over eight minutes left of the first period, Lukko looked to be on course for a routine win when Ponthus Westerholm made it 3-1, and that's how it stayed until the 20-minute mark despite multiple powerplays for both teams.
The second period saw an end to the penalties, but also to the Lukko dominance, as the only goal arrived in the 17th minute, when a sustained period of Pelicans attack resulted in Michal Jordan squaring the puck along the blue line for Einari Luhanka to fire past the goaltender.
And the Lahti side stunned the home crowd by completing the comeback in the seventh minute of the third, as Daniel Nieminen scored unassisted. No further goals despite 15 shots on target from Lukko in the third period alone meant overtime would be required.
With 01:24 on the overtime clock, the Rauma side got the winner their late pressure perhaps deserved, as Steven Jandric and Antoine Morand combined, and when Morand's shot was saved, Eric Galinas followed up to score on the rebound and win the match, 4-3.
Lukko may have only taken two of the three points on offer, but they have at least closed the gap with leaders Tappara to seven points, while Pelicans are now three points shy of the Playoff places despite their lack of recent victories.
