Despite the early pressure from the hosts, it was the Addicks who managed to find a breakthrough.
Iceland's Gudmundsson cut inside from the right and fired a powerful shot from distance, beating Loach at his far post.
Rotherham began the second half with intent and did not have to wait long for their reward as substitute Ben Pringle found Becchio, who headed home to score his first goal for the Millers and first since January 2013.
Belief began to sweep through the Rotherham ranks as they pushed for an unlikely winner. There was a penalty shout from the hosts in the 80th minute, but only half-hearted appeals from most.
The final 10 minutes saw Rotherham hammer at the door looking for what could have been the winning goal, only for Charlton to come close to nicking it.
A Jordan Cousins cross crept under Loach and came very close to crossing the goal line.
Lee Frecklington was almost the Rotherham hero in the dying moments when his left-footed effort skimmed the crossbar and landed on the roof of the net.