© PA Photos
Neil Lennon's side were in control of the match right from the start and went ahead on 19 minutes when Gary Hooper latched on to Georgios Samaras's cross from the left and shot home from inside the United penalty area.
Wanyama came close to scoring his second goal of the evening just before the half-time interval, and Samaras and Hooper had chances to add to the tally after the break.
Hooper and Samaras combined for Celtic's third goal on 80 minutes, the former once again turning in the Greece international's pass from close range.
Scott Brown added the icing on the cake for Celtic with their fourth goal of the match four minutes later, this time Hooper being the provider.