Wanyama made sure of the points with a superb strike four minutes after the breather to ensure Celtic triumph in an entertaining match at Celtic Park
The bottom placed team seemed to have a credible game plan of keeping the Bhoys at bay, but it only worked for 39 minutes, when Neil Lennon's side were awarded a penalty. Scott Brown's spot kick was saved by Rob Doughlas but Gary Hooper arrived first to tap in the rebound.
Wanyama made sure of the points with a superb strike four minutes after the breather to ensure maximum points for Celtic, who had only managed to share the spoils with Benfica in their opening group stage match of the UEFA Champions League in midweek.
The result sees Celtic maintain their grip on the standings of the Scottish premier League, a point adrift joint leaders Motherwell and Hibernian. Dundee remain in the relegation zone.