KuPS were on the back foot early on in the game, but settled their nerves midway through the first half when Mohamed Toure broke the deadlock with a poacher's finish.
The Guinean delivered a sucker-punch to the Kotka side late in the half, picking the ball up on the edge of the box, turning his marker and hammering the ball past the goalkeeper.
The Kuopio club wrapped up the 3-0 win just before the hour mark - Toure was denied his hattrick by KTP goalkeeper Maxim Zhukovsky, but Otto Ruoppi was on hand to gobble up the rebound.
The sorry afternoon for KTP was compunded by a second booking given to Uhro Huhtamaki with 20 minutes to play, as they remain one from bottom in the standings.
SJK's brilliant start to the season is well and truly over as they suffered a second straight defeat, this time to VPS on Monday night, who left Seinajoki with a 3-2 win to move fifth in the table.
Mads Borchers was fouled in the area in the opening minutes, and he took responsibility from 12 yards to give VPS the lead.
Having lost the top-of-the-table clash with KuPS last time out, SJK finally seemed to have rediscovered the form that had taken them there in the first place, when close-range finishes either side of the break from Rasmus Karjalainen and Jeremiah Streng turned the match around.
But the Vaasa side were never out of it, and few were surprised when they equalised after the hour mark - even if no one saw Yassine El Ouatki rifling the ball into the top corner coming.
SJK were looking the more likely to find the winner, but in added time, the OmaSP Stadion crowd were silenced when a flick on found Borchers, who found a way past goalkeeper Roope Paunio despite the tight angle.
His two goals put the Dane top of the scoring charts in the Veikkausliiga, and secures a second consecutive win for VPS.
Elsewhere, Inter Turku remain third and unbeaten, but were disappointed not to take all three points away at Mariehamn, instead coming from behind twice to draw 2-2.
Now level with Inter on 12 points are Ilves, who threw away a 2-0 lead at home to Haka, only for Aapo Maenpaa to pop up at the back post and force a 90th-minute corner over the line to win it 3-2.
Having lost their first three matches, HJK have steadied the ship by taken seven points from their last three and moved up to seventh. Their latest outing saw three second half goals away at Jaro to win 3-0.
AC Oulu got their first three points last week and were on course for a win over Gnistan when they went 2-0 up after 50 minutes, but a brilliant comeback saw the visitors turn the match on its head and win 3-2, with Juhani Ojala scoring the winner three minutes from time.
Oulu are still propping up the table, behind KTP and Jaro; Gnistan move onto nine points and sit sixth, two points ahead of HJK, Haka and Mariehamn.