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Celebrating the club's centenary, Banik Ostrrava took an early lead through Eidar Sehic. The goal appeared to spark Postecoglou's side to life, Japanese star Kyogo Furuhashi netting an equaliser just six minutes later.
Celtic manager Ange Postecoglou reflects on pre-season Czech-mate
On 24 minutes, Celtic took the lead, David Turnbull threading the ball through to Matt O’Riley, who fired his shot past the Ostrava 'keeper to put the visitor in front.
Enjoying 70 percent of possession, Celtic went 3-1 up just after half-time, when Anthony Ralston's cross was volleyed home by Giorgios Giakoumakis.
The home side hit back midway through the second stanza through Muhamed Tijani but three minutes later, Celtic restored its advantage through Liel Abada, who followed in Giakoumakis's parried shot to seal a comprehensive 4-2 win.
Postecoglou's men are next in action at home to Blackburn Rovers on Sunday (AEST).
CELTIC: Hart (Siegrist 65), Juranovic (Ralston 46), Carter-Vickers (Jullien 60), Welsh (Lawal 60), Taylor (Bernabei 46); McGregor (McCarthy 60), Turnbull (Johnston 60), O’Riley (Ideguchi 46), Jota (Maeda 46), Kyogo (Giakoumakis 46), Forrest (Abada 46).
Subs: Bain, Oluwayemi, Ajeti, Kenny, Urhoghide, Vata