The Thessaly club have been stuck on 11 points since Nov. 13 but Kostenoglou, who joined the club after Jorn Andersen's 24-day reign as coach, led them to a 2-1 home win over Iraklis Thessaloniki.
The bottom club's first win since October lifted them to 14 points, five adrift of safety.
"We knew it would be very difficult game, but victory was our only option," Kostenoglou told reporters.
"We achieved a very important win which is crucial both for our psychology and in trying to do to close the gap in the league table. We have a permanent struggle on our hands which needs focus and discipline."
Jan Blazek put Larissa ahead in the first minute before Apostolos Vellios pulled a goal back just before half-time. Congo forward Joel Tshibamba netted the winner with just nine minutes left.
Elsewhere, leaders Olympiakos retained top spot with a 4-2 home win on Saturday and champions Panathinaikos defeated Kavala by the same scoreline at the Olympic Stadium.
French striker Djibril Cisse continued his exceptional form for the Greens with another double, taking his tally to 16 in 18 matches. Kostas Katsouranis and Lazaros Christodolopoulos were also on target for the hosts.
Olympiakos, who have 45 points, lead Panathinaikos by five points, while PAOK Thessaloniki remained third on 30 after defeating Olympiakos Volos in a match marred by crowd violence on Saturday.
The kick-off was delayed for 30 minutes after a small section of the Panthessaliko stadium in the Thessaly city of Volos was damaged by fire as authorities tried to remove PAOK supporters who attempted to enter without tickets.
AEK Athens are level on points with PAOK after winning 3-0 at struggling Asteras Tripolis whose coach Vangelis Vlachos left the club after the match.
