Slovenia's Simon Spilak kept his one second lead over Tour de France winner Chris Froome in the overall standings.
Albasini, who had already won the first and second stages on Wednesday and Thursday, beat Frenchman Thomas Voekler and Jan Bakelandts of Belgium in a sprint finish among the five-man escape group, that included two more Frenchmen, Alexis Vuillermoz and Jean-Marc Marino.
"Before the Tour of Romandie I would have been happy with one stage win so three is a bit crazy," said the 33-year-old Albasini.
"After this I'm going on holidays so I'm trying to give it my all during the race."
The Swiss rider's win continued his Australian Orica-GreenEDGE team's fine form this last week, with young Briton Adam Yates leading the Tour of Turkey having won Friday's sixth stage in that.
Australian Simon Gerrans also claimed victory at Liege-Bastogne-Liege last Sunday for Orica.
Katusha's Spilak had taken the leader's yellow jersey off Albasini by outsprinting Froome to win Friday's mountainous third stage.
Sunday's fifth and final stage is an 18.5-kilometre individual time trial around Neuchâtel, in which Froome will be the overwhelming favourite to retain his title.
The last three winners of Romandie -- Froome, Bradley Wiggins in 2012 and Cadel Evans in 2011 -- have gone on to win the Tour de France.