That point took the visitors' tally to 10 from four games, seeing them sit in second spot in the Turkish Super Lig table, while their hosts dropped to 13th after a defeat to Kayserispor last time out.
After last season's 14th-placed finish, Kasimpasa began the new domestic campaign with a trip to Hatayspor, and they left with a point as Saba Lobzhanidze levelled the game in the 72nd minute for the hosts after Valentin Eysseric's early opener for the Apaches.
Senol Can's men then quickly put their first win on the board, as Nicolai Jorgensen and Umut Bozok fired them to a 2-0 home victory over Giresunspor, before they earned a particularly impressive draw in a clash with title-chasing Galatasaray.
First-half goals from Alexandru Cicaldau and Kerem Akturkoglu seemed to have all but won the game for the 22-time top-flight champions, but Jorgensen pulled a goal back on the stroke of half time, and Bozok netted an equaliser soon after the hour mark to see them take a commendable point on home turf.
After a strong start to the campaign, the Apaches will now look to bounce back from that loss, but they face another tough test as they welcome a Trabzonspor side in impressive form.
The visitors arrive with 10 points from their opening four games of the league season, having started with a dominant 5-1 away win over Yani Malatyaspor, as Anastasios Bakasetas, Anthony Nwakaeme, Gervinho and Marek Hamsik all got on the scoresheet in the first half before Djaniny converted a penalty to cap off an impressive showing.
On the back of a 2-1 defeat to Italian giants Roma in the first leg of their Europa Conference League Qualifying tie, Abdullah Avci's side made it two wins from two in the Turkish top flight, as Bakasetas and Nwakaeme fired them to a 2-1 home victory over Sivasspor, before their European fate was sealed with a 3-0 defeat in the second leg in Italy.
Karadeniz Firtinasi did not seem fazed by that defeat though, as they returned to league action to beat Giresunspor 1-0 away from home, with Nwakaeme again finding the net, before earning an impressive point in a 2-2 draw with Galatasaray last time out.
Similarly to their opponents' clash with the Turkish giants, Trabzonspor fell two goals behind before the break, but Andreas Cornelius pulled them back into the game before Nwakaeme hit his fourth goal of the season to see Avci's men remain unbeaten.
They will now look to extend that to five games and make a quick return to winning ways in order to further establish themselves at the top end of the Turkish top flight.
They will also be missing midfielder Valentin Eysseric, leaving Can with a gap to fill in the engine room.
Nicolai Jorgensen will lead the line with confidence, having netted two goals in his first four appearances for the club.
Trabzonspor boast plenty of quality going forward, with Andreas Cornelius leading the line, while winger Anthony Nwakaeme has found the net in each of their first four league games of the season.
Former Napoli star Marek Hamsik also offers additional threat in the final third, and he got off the mark for the campaign on the opening day.
They will continue to play without winger Gervinho though, as the Ivorian recovers from a knock, and he is joined in the treatment room by Djaniny and Anders Trondsen.
Kasimpasa possible starting lineup:
Taskiran; Hadergjonaj, Bruma, Serbest, Elmali; Travnik, Sadiku; Erdogan, Hajradinovic, Dirar; Jorgensen
Trabzonspor possible starting lineup:
Cakir; Peres, Hugo, Ie, Koybasi; Ozdemir; Omur, Hamsik, Bakasetas, Nwakaeme; Cornelius
We say: Kasimpasa 0-2 Trabzonspor
Despite the hosts' relatively impressive start to the season, we think Trabzonspor will have too much firepower on Saturday.
With the likes of Nwakaeme, Cornelius, Hamsik and Bakasetas forming a well-oiled machine in the final third, Kasimpasa could be overrun, and should certainly be outclassed by their visitors.