Colombian striker Joeo Rodriguez missed a golden chance to win the match when he sent a shot agonisingly wide from six yards in the 80th minute.
Senegal were always a physical threat from set plays while Colombia dominated possession, but lacked a little quality in the final third in difficult conditions.
The colourful Hamilton crowd of just under 4000 didn't let the rain steal their party as they sung and danced their way through the 90 minutes.
Powerful striker Thiam always looked dangerous for Senegal while Rodriguez was a constant threat with clever footwork for Colombia.
Colombia, who sit on four points, will next face Portugal in a match that will determine the Group C winner while Senegal must beat winless Qatar to progress to the round of 16.
Senegal 1 (Mamadou Thiam)
Colombia 1 (Alexis Zapate)
HT 1-1