The turning point of the game came in the final minute of the half when Langfield was sent off after bringing down Georgios Samaras inside the area.
Commons stepped up to take the spot kick and fired the ball down the middle to give the visitors the lead heading into the break.
Samaras should have added to Celtic's lead at the start of the second half but fired a volley over from close range after Aberdeen had failed to clear.
The home side had their best chance of the game in the 52nd minute when former Celtic winger Niall McGinn met a cross from Jonny Hayes, but his headed effort was saved by Fraser Forster.
Forrest added a late second for Celtic when his effort took a deflection and looped over keeper Nicky Weaver to seal victory.