A draw at home would be enough for the Veikkausliiga champions to proceed after they won the first leg 2-1 away in Riga last week.
That was exactly what they were heading for, as despite pressure from Petteri Pennanen and Mohamed Toure, KuPS could not find a route through the RFS defence, while not allowing a shot on goal at the other end, although a great Ibrahim Cisse block was needed to deny Barthelemy Diedhiou.
But things could have been very different without a VAR intervention in the final 10 minutes of the half - referee Balazs Berke pointed to the penalty spot after Diedhiou went down in the area after a coming together with Bob Armah, only for the decision to be overturned following the review.
Following the reprieve, Toure tested Marko Maric from range with time winding down, but the goalkeeper saved comfortably to ensure the sides went into the break level on the night.
However, Maric was powerless to stop KuPS breaking the deadlock four minutes into the second half, when Toure's pass from the left found Otto Ruoppi, and he laid it back to Pennanen, who curled in a first-time 20-yard effort off the post.
With just over 20 minutes to play, Toure went down in the box under the challenge of Aleksandar Filipovic, but penalty appeals were waved away. Soon after, the Latvian side came within a whisker of an equaliser, as Stefan Panic's header came back off the post.
But the Kuopio side held on not only for the win and clean sheet on the night, but a 3-1 aggregate victory.
The only downside for KuPS was a nasty clash between goalkeeper Johannes Kreidl and teammate Samuli Miettinen in injury time - both needed lengthy treatment and needed to be replaced, though both were able to walk off the pitch.
In the Playoff Round, KuPS will likely take on Danish side FC Midtjylland, with the winning progressing to the UEL League Phase, while the loser will drop into the League Phase of the UEFA Conference League.
Meaning the Finnish side are now certain to reach a European competition proper since playing in the First Round of the 1990/91 UEFA Cup Winners' Cup, which didn't require navigating qualifying rounds.