The Kenyan, influential in the Harambee Stars 2-1 loss to South Africa in a friendly match in midweek wa at his best at St Mirren Park in an easy win for the Hoops.
Four of the goals were scored in a stunning first half display.
Gary Hooper opened the scoring on 15 minutes with Nigerian defender Efe Ambrose added a second three minutes later.
Six minutes apart
Wanyama then took over with goals in the 32nd and 38th minutes.
Teenager Anthony Watt finished off the scoring four minutes from time.
Celtic (20) have a five point lead in the league over second placed Hibernian as they look forward too UEFA Champions League action in midweek.