The SHL league leader has never succeeded in the Champions Hockey League and this year's semifinal spot is the best so far in seven seasons.
But there are good prospects that it will be better than that.
Färjestad won the first semifinal at O2 Arena in Prague after a dream start.
Only 99 seconds had been played when Viktor Lodin steered in Magnus Nygren's shot to 1–0.
Sparta Prague equalized through Jani Lajunen, but Färjestad took the lead again through Oskar Steen before the first period was over.
Färjestad could then extend their lead through comebacking Alexander Ljungkrantz in the second period.
In the final period, the visitors pulled away through Marian Studenic, Oskar Steen (with his second goal) and Joel Nyström.
A form-topping Studenic, the Slovak forward, was credited with a goal and three assists.
Färjestad played without injured star player David Tomasek, who has Sparta Prague as his parent club.
The return match in Karlstad is played next Tuesday and the aggregate score over two matches counts.
In the other semifinal, there is an all-Swiss meeting between Genève-Servette and ZSC Lions, and the first match is played on Wednesday.
The final is decided in one match and is played on February 18.
