KooKoo would have been confident of extending their winning run to five matches and going level with second-placed JYP, only to find themselves 2-0 down after seven minutes, following Otto Hokkanen's powerplay goal before a quick second from Janne Naukkarinen.
The home side's confidence grew in the final five minutes of the opening period, when Jimi Suomi got them on the board.
But not only could the Kouvola side not find a leveller, they fell two behind again with six minutes left in the second, as Patrik Siikanen made full use of another powerplay to make it 3-1 to SaiPa.
Yet whatever Siikanen could do, Miska Siikonen could do too - he closed the gap with another powerplay effort late in the period, and this time KooKoo completed the comeback seven minutes into the third, through Santeri Sulku.
Amid a spate of penalties in the final 20 minutes, it was inevitable that a powerplay goal would settle matters, and with less than two minutes to go, Siikanen grabbed his second of the evening to win it 4-3 for SaiPa.
Not only did that goal end KooKoo's winning streak and keep them in fourth place, it put an end to a run of three losses in a row for SaiPa.
Two goals were enough for Lukko to move back ahead of JYP and into second place on points difference, as they beat Jukurit 2-1 away from home.
Mikael Ruohomaa's opener for the visitors in the first period was cancelled out by Jesper Piitulainen's equaliser late in the second. But with four minutes to play, defender Jirko Tukiainen popped up with the winning for the Rauma side.
A third loss in four keeps Jukurit just two points inside the Playoff places, while four successive wins puts Lukko six points behind leaders Tappara.
That's because Tappara earned a 2-1 win of their own at home to Hameenlinna, who returned to losing ways and remain one from bottom, three points outside the Playoff picture.
Goals in the opening minutes of the first and third period - from Benjamin Rautiainen and Jyrki Jokipakka, respectively - put the Tampere side clear before Cameron Wright added a late consolation.